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Probleml: Use the points A = (,-1). B = (1,-9), and € = (1,2). Find the eqjuation of the line AB , Ad the line A8 .Problem2: Write An e(uation t0 find where t...

Question

Probleml: Use the points A = (,-1). B = (1,-9), and € = (1,2). Find the eqjuation of the line AB , Ad the line A8 .Problem2: Write An e(uation t0 find where the line y Tr + ! interseets tie line V = % Solve vour equation. Sketch graph:Problem3: Write the eqquation of a function that takes AS input Hher & , Ad outputs twice tie distace romWrite the (quation J() =|-1-2+I as A pieeewise funetion and graphProblemA: Find the solution St of each eualitv Ad draw picture to illustrate cchi situati

Probleml: Use the points A = (,-1). B = (1,-9), and € = (1,2). Find the eqjuation of the line AB , Ad the line A8 . Problem2: Write An e(uation t0 find where the line y Tr + ! interseets tie line V = % Solve vour equation. Sketch graph: Problem3: Write the eqquation of a function that takes AS input Hher & , Ad outputs twice tie distace rom Write the (quation J() =|-1-2+I as A pieeewise funetion and graph ProblemA: Find the solution St of each eualitv Ad draw picture to illustrate cchi situation 4-I=y+1 Problems: Express the solution set of each inequality in interval notation AIdl draw picture t0 illustrate each problem 1, 312r + I/2r+1 2 V-I<r+1|



Answers

Match the description with its graph. Determine the slope of each graph and how it is interpreted in the given context. [The graphs are labeled (a), (b), (c), and (d).]
A school district purchases a high-volume printer, copier, and scanner for $\$ 25,000$ . After 10 years, the equipment will have to be replaced. Its value at that time is expected to be $\$ 2000$.
(a) Write a linear equation giving the value $V$ of the equipment during the 10 years it will be used.
(b) Use a graphing utility to graph the linear equation representing the depreciation of the equipment, and use the value or trace feature to complete the table.
$\begin{array}{|c|c|c|c|c|c|c|c|c|c|}\hline t & {0} & {1} & {2} & {3} & {4} & {5} & {6} & {7} & {8} & {9} & {10} \\ \hline V & {} & {} & {} & {} & {} & {} & {} & {} & {} & {} \\ \hline\end{array}$
(c) Verify your answers in part (b) algebraically by using the equation you found in part (a).

So here we have graft, a scatter plot based off the points given to us on the table. And now we need to find the equation of the line of best fit based off of two points on this scatter plot so we can choose any two points. Just be aware that if you choose to different points, you may get a slightly different equation for your life. So I'm just going to choose this point on this book. So we have negative 30 10 on and negative 14. 18. So now we need to find the equation of the line of best fit. Now, remember, the equation of a line and slept in except for him, is why equals m X plus B. So what we need to do is we need to self, um, and for B So, um, is the slow and we know the slope formula. So I just got right down here, um, equals y two minus. Why one over x two minus X one. Now it doesn't matter which one is x one y one or x two y two. So I just do they say this x one? Why one next to why to. So we have 18 minus 10 over. They get a 14 minus native stay the negative 14 plus day. So we have it over 16 which identifies 2 1/2 So now we need to solve Would be. What we can do is we can plug in this em into the equation. So we have. Why equals 1/2 x plus b not order yourself a B. We need X and Y values. What we have accent wise. These are simply points that are going to be on that line so we can choose anyone. So when she was negative 30 and 10 for X and Y voice. So we have 10 equals one have Ah ah! What half times that you have 30 plus b. So we get 10 equals negative, 15 plus b. So we get B equals 25. So fire equation is why equals 1/2 X plus 25. Now we can compare this to the equation of the line of best fit found using a graphing calculator. Now I can't tell you exactly how to find the line of best fit, but im sure theres a linear regression program on your graphing calculator. that you can use. And as you see if you're using, does knows I got why equals zil 0.44 x plus 23.5 and that is roughly close to why equal.

Okay, so this one says, if the two lines interested at point a B, what is the value of a plus B? Well, so let's go in and try to fill in the information that we know. We know that one of the lines have a slope of two and goes to the point. Welcome. Eight. Well, we know that our equations you're all in with the form of y equals MX plus b r m is our smoke and B is our by Anderson. So if it already tells us that our slope is too, you know, it's why is equal to two x plus B and we just have to find that intercept value. So from there, Reznik in order to find out what this pluck in this point. But it goes through as the X come alive two times. One plus B is equal to eight. Now we know that Khun subtract two from both sides. Giving us that six is equal to be so. In order to complete this equation, we know that it's just going to be six to expose six. So that's our first equation on that. We know that the second equation goes through one color one and two come one to them again. We still have to find our vehicles and most sports peace. I'm going to start out by finding this slope. No defender Slipper doesn't do y two months. Why one over X to minus X one. That's gonna be one minus two over to minus one, which gives us negative for one. So from there, I know it's going to be wise Eagle to negative X plus B. And again, we could just put in any of those points. So I'm going to go out and plug in that first point one comma two, at which point we got to a sickle to negative one plus B. So then, if we add one to both sides, we get that b is equal to three. So our second equation is going to be Y is equal to negative X plus three. So here's our first equation, and here's her seven equation. So then we know that they interested at this point so foot intersex than we have to find thie ex coming. Why, after we've come combined the two equations. So here's our second equation. So I'm going to just go and use substitution to set these two equations equal to each other because this's ableto and that's what's why. So I was going to happen equal to each other. To have two X plus six is he wants necklace expose three. I'm gonna add extra both sides giving me three acts and then I'm gonna subtract six from Besides giving me negative three So x is equal to negative one because I divided both heads back to me. But again, if we're looking for a plus B, we also need the bee value, which is our Why about you? So I'm going to put this back into any overy equations and who's going to plug it into this one, and I'm gonna get that y is equal to negative of negative one plus three negative negative cancels out. That gives me four. So here now we have our why value and our X value. So our guess values right here or y values right here. If we add them together, we got three. So B is our answer

We were given an objective function in the system of linear inequalities. The objective function is Z equals 10 X plus 12 y, and the linear inequalities are X is greater than equal to zero. Why is greater than reporters? Hero ex post wise less than or equal to seven two x plus wise less than or equal to 10 in two X plus three y is less than or equal to 18. In part, they were asked, Graph this system of inequalities noticed that X is greater than any quarter zero and why is greatly record zero? So if the solution exists, it will lie in the first quadrant autographed the third inequality in Red. A graph this autograph X plus y equals seven. First. If X is equal to zero, we have that y is equal to seven. And so we have a Y intercept at zero seven. And if y z quarters here we have that X is equal to zero. I mean seven. So we have an X intercept at seven zero. And because this is a solution, I'll draw a solid line between these two points. I'll use the origin is a test point zero is less than equal to seven, so everything to the left of this red line is a solution. I'll graph Inequality four and green. To do this autographed two x plus y equals 11th. If y is equal to zero, we have that X is equal to five, so we have next intercept at 50 If X is equal to zero, we have that y equals 10. So we have a Y intercept at zero 10. And because this line is a solution, I draw solid lying between these two points I'll use the origin is a test. 0.0 is less than equal to tend, so everything to the left of this green line is a solution. Paragraph Inequality five and blue do this Paragraph two x plus three y equals 18 1st If y is equal to zero, we have that X is equal to nine so that we have an X intercept at nine zero. And if X is equal to zero, we have that Y is equal to six. But we have a Y intercept at zero six, and because the line is a solution, I'll draw solid line between these two points and I'll use The Oregon is a test point, since zero is less than or equal to 18. If all is that everything to the left of the blue line is a solution. And now in black, I'll draw the solution to the system. So this includes from here, down to here, over to here. To here it appears as if three lines might be intersecting in one point. We'll have to check this, but we have that this shape, which is a quadrilateral. This region is the solution to the system of equations. You're inequalities and has Vergis ease at 00 at 50 Not sure what this one is yet and this one is going to be zero six. So what is this mystery Vergis E To find the answer, let's first find the intersection of the red and green lines. So we have the X plus y equals seven in two x plus y equals 10. Insult this by simply subtracting equation two from equation one. We get X minus two exes native X Y, minus Y zero and seven minus 10 is negative. Three. So that X is equal to positive three and by back substitution why is equal to seven minus three, which is four. Okay. And to see if this really is just one point of intersection, what's also on the point of intersection between the Green Line and the blue Line? So we have two x plus y equals 10 and two x plus three y equals 18 Sold. This simply subtract equation two from equation one. We get two X minus two x zero. Why minus three Why is negative? Two y and 10 minus 18 is negative. Eight. So we get that again. Why is equal to four and we have by back substitution. That X is equal to 1/2 of 10 minus four, just half of six or three. So these are indeed the same point, so we only have one point in their section here. Between all three lines, which is the point 34 in Part B, were asked to find the value of the objective function each for Tex of Region at 00 Value of Z is zero at 50 Value of Z is 50. At 34 the value of Z is 30 plus 48 which is 78 and at 06 The value of Z is 72 and in part C were asked to use the information from Park Be to find the maximum value of the objective function, the corresponding values of X and Y. We have a theory that says that if a maximum for the objective function exists in this region determined by this system of linear inequalities, then a maximum will occur. At least one of the vergis ease of this region and so looking at part BBC at the maximum must be 78 which occurs at 34

You asked to find, uh, the question off the line off the home y equals MX les bee. Okay, that's our But each of these cases, we have ah, 55 sections in the, uh, this question You. So in the first case, it passes through their told that it passes through two points through seven minus seven minutes to and little little the passage from minus seven and little little. So I think we know what the hell were done from the questions in the past. But I m on. We need may all these cases All right, So and and miss and rinos white, why one guarded by extra My no sex one. The extent of this election woman was sick the way too. We have by 20 minus honest too. Lettered by extra Zittel minus X one, which is minus seven. I have answered us who over and the best way to find out the value of people. We found a value of em to get the value of B. It's simply substitute that know the value, that because this court for him in this equation and you can use any of this corner Well, why excellent like that's become so that Ben what happened? They get let's use 00 and then late. Why equals who was seven? It's unless the use this blacks and why the little by seven of people, I think. Which means the old So is there a venues moment it passed through the origin. But just look bugging in the values. Therefore, you're finally questions. Why equals 17 x these ill It crops up and weaken. Very fired us. You're already fired by You can substitute. They do seven negative through to the mission and see that it satisfies this condition. Have been wise minus two. That's minus. Still, there were seven off minus seven. Also it's minus two, I think now. Okay, this again. It buses through six months street and has a y intercept a week. But who I think different. The buses through six months seat and has away in the SIPO. Why that's set off eight. That they have a lead like that. Why in consider plus eight it was eight. It's going to this links which would be but this way, this way that were any of those things, but also passes offsets minus three of you know, six is sexist radio and mine a second built here. So that's the second point There's a line. Looks something like that six minus and this distance is eat. All right. Anyway, so those are just just a graphically get to give me the airport how the line looks like. But let's start with a mix of like was it makes us be, And then they got them and be that we need m and B toe the indication, But we're told that process for six minus street. Well, personally, the fact that it has a way of Cassa per week, they know that the secretion be represents the wine because the next zero, why it would be so the next zero y could be an artist. The receptor. This is just a list of the village with straight. We can on this lying from that the words that you should you should know that B equals eight. Okay, so then the question becomes bike one. Yeah. So? So the question is why equals m X less ache the business where we're next. What about him? So to financially, simply used a packet passes through of six Minutes Street. So it's like in six minutes sleep. Oh, except White. So why it's minus three. So used. That money equals and was unknown. Xs plus six. But they So we get six. Emma plus Peak. And then that means you subtract it from both sides, and I get minus 11 equals six. I m senior M equals minus 11/6. Well, it seems with right back, but it's not the best of numbers, but it is what it is and Emma's made So which is Nixon? See? The likely Drew also is, as a is an acute angle, so that would agree well with Mbali. Negative in value. OPEC. Now let's go back and play gender on medication so therefore, finally questioned, why equals minus 11/6 x last eight and does it? Let's leave Verify. This is let's plug in value of six for this group of minus 11/6 times six is minus 11 plus eight of minus three. And at this point for a good answer, the production go down. Okay, but then we're going to see they hear. The question is, it passes through zero minus one, and as the same slope as the line. Breakfast for y equals Well, okay, you two pieces of information here when it passes through zero minus one. That's the first book. And same slope s as a different line. It has same scope as a line three experts for by equals Well, same Klopas, The Line three X. That's four y equal Strel. Okay, let's I use just carefully. The three expert forward equals 12. We do We know the slope off the line from this equation. I think they used to sing this off a pompous equation of the form. Let's in this case why it was precisely in this in why equals MX plus B. We know that this is the stroke, Ramos a slope. But we have a slightly different different formula. Three experts for Waple smoke. But what? The first thing we should do it before doing, taking any guesses, convert this to this boat, okay. And then just well, aren't the value and look at the presence. Okay, well, that's You should not just blindly go, but they prohibition toe X ss look, which will give you a value of plea. But remember, that is not the this question is not for the farm. White was an extra speak the coefficient of why in this is one. But as this kid is full So that's what we need to be toe 100. This to the family coefficient of y 21 and then read off the value the coefficient of X. Give us 10 million. So to do that for way Question, let's review the Aries and like you said or y equals well, a minus three X, isn't it okay, Impact to be more precise, fishing practices minus three X less Well, if any, given this fall, the four wake was this. And so why equals doing before on both sides, honestly, before less 3 November for every time before. Okay, now we already. Now, if you compared this and this room, we know that Emmis and is minus 3/4 and not do you not just three. So between zero minus one of the first point putting back to a question and we can refer also slope as an M equals minus 3/4. Okay, now that's right. Take waiting for this guy. No. Now we are ready to find the writer dictation of our line of interest. This is a different life on it. Princesses. But the slope of that lines. And we say, Okay, the scope of online it's the same as this. Okay, in other words, outline and the sign of battle. Okay, the old later start going back of this hiss our Linus. Now the rial y equals M X plus B off the foam labels and extras. B you know, I must neighbor three or four, but native, 3/4. It must be. Now we know it passes through zero minus one. Well, it's like in the values for excellent wife using these coordinates. Why is minus one sequence minus the over four times zero? That's zero. Blessed be. And so, which means May it quits minus one. There's no equation becomes I know why equals Emma's ministry over for its plus being that minor, that recognition the vehicle and my club. What part of your question is the passage of 62 and has the same X intercept as the light minus two expressway? On this, Take this piece of information slowly, you're passes through 62 Let's write that down that passes through six to right and and has the same X intercepted minus two explains. Why was one minus two x less why he would want. That's a different line. That's the same eccentricity as this. The betweens, this line as next final workers. The X intercept of slime, The X intercept. Pretty Norman. We have something like this and accept disapproval. Linus of any other troubling many. Linus, let's It's just like that The X intercept at that distance distance where? From the orders in to the point there. Why is there at that point? Okay, if you have a different line like that, the X intercept this like the set of this. But this line is that arrested that Listen that so in other words, just make y zero get the value of it. And that's what we do here on the X intercept of this line you make Why equals the little and then it means minus two X equals one index. Iqbal's. No, you don't help. But this line I just talked to a random lines. The ex sequence minus half. Okay, All right. So let's do the same thing for this meal coming back to all equation. Why equals MX plus big. All I know when you making wives, it'll right. So that means this line passes through this line. Passes to minus have zero. It is, in other words, we're pretty this line. The information we got from this is that old line also passes through making you have zero online. Could be this this, this this I don't know because we don't know the slope. Okay, but what we know from here is another point. This minus, uh, little. Okay. Or now we know how to solve. Get the equation off the line was to with much. Two points are known. What do we do that let's cited, why equals But this user, the infallible this biotech business way because the mix would be and figure out all right, I m no And this white humanise by one. Doing by extra miners X one. Okay, pick zero minus. Who? Led by miners hop minus six. Okay, so that would be a little ministered. Minus two divided by, uh, this is 13 over to minus 13 over to, or this EF minus $2 bill one developed by Minister King over to it is the same as minus still over one times two over minus 13 like this. More over 30. Wow. So but one of the and again looking numbers. But but then aside, the question of life was our slippers for over 13. The Michaels that's less be they get. Be able use Ah, minus zero because natural this visited. So if he used using minus have zero the legend of the sick nation, we get zero equals for over 14 kinds minus. Let's be no to induce us minus 2/13 Le Thank Middle, in other words, be is to over 30 and therefore our equation becomes Why equals MX m is for over 13 for over 13 x must be based to with less two over. Okay, how quickly, uh substitute and see if it's true. So for this point, it's negative. Have access, negative. Have. And so that's negative. To over 13 plus totally makes zero. The other point. We have a six to that 6 to 7 for this equation we're taking roll. The sticking of this equation is kind of if you put whitener to okay, lets fanciers to, and then I can decide this for over 13 times six. That's to over 13 which is 24 or between plus two bean, which is ballistics. Over between with this in lead to okay, that is our good and sections for bill training. Listen, it could be the real or liquid revealed studying why equals or express to, and that would make it look nice, But I think we'll ask to This is the same as 13. Why equals four X plus two politics plus two or another way of reading. This is morning minus studying. Why? Plus two equal silk. That would be the same. A better way of better the petition off. Okay. And to e has exodus of minus six. Y intercepts were, too, though our exit disip of minus six. And why intercept off Weld to Okay, All right. Okay, so that's this information. So you know that, uh, the line goes like that? That's the X intercept. And that's the white visit, right? So assuming that Arctic creationists begin white was MX less beat. We know that b is the language in this film. And help from Y S. T. B is the latest, which is weird given in this square. So that's straight away. Ask weather and X in cusip of minus six means on my door like a positive exercise. When? Why is it so? Thank you's minus six. So then what is it'll? We're going to begin. This isn't this is packed with it. This means when life zero rent Nazi then why is And like with zero right? Whatever little X you consider this a critical toe minus six except the cycle Samos X value. That's really world seven ways it'll. But that's youth. This make was zero one and we excellent benefit before must be spared too. Okay, What this means this means minus 6 a.m. less well, two equals zero. And with means squared two equals six him You are m iss ready to order by and that the loosest information The frame are a mix of the line. The question why z quinto Emmis six Thanks Les Bee


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