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Warm _ ~ Up4) Graph AB with coordinates A(*2.+5) and B(6.-[). b) Graph CD with coordinates C(-1.3) and D(2 3). c) Find the slope of AB and CD d) Are the lines para...

Question

Warm _ ~ Up4) Graph AB with coordinates A(*2.+5) and B(6.-[). b) Graph CD with coordinates C(-1.3) and D(2 3). c) Find the slope of AB and CD d) Are the lines parallel o perpendicular?Explaination:2Graph AB with coordinates A(-1.4) and B(2.6). Graph CD with coordinates C(I.0) and D(4.2). c) Find the slope of AB and CD Are tle lines parallel or perpendicular?

Warm _ ~ Up 4) Graph AB with coordinates A(*2.+5) and B(6.-[). b) Graph CD with coordinates C(-1.3) and D(2 3). c) Find the slope of AB and CD d) Are the lines parallel o perpendicular? Explaination: 2 Graph AB with coordinates A(-1.4) and B(2.6). Graph CD with coordinates C(I.0) and D(4.2). c) Find the slope of AB and CD Are tle lines parallel or perpendicular?



Answers

Graph pair of lines. Use slopes to determine whether the lines are parallel, perpendicular, or neither. $\overleftrightarrow{A B}$ and $\overleftrightarrow{C D}$ for $A(2,-1), B(7,2), C(2,-3),$ and $D(-3,-6)$

Here we have the equation, the line. And let's start by converting the equation into slope intercept form so we can subtract X from both sides. And we have why equals the opposite of X Plus four so we can see that the slope of this line is negative one, and any line parallel to it will have the same slope. So the parallel line will also have a slope of negative one, and any line perpendicular to it will have the opposite reciprocal slope, so a perpendicular line will have a slope of positive one.

Points four points are given a me C. N. D (472) 513 and -11 4725 13 and -11. Right now let's say for the line A. B. Let's the question like maybe so this can be written as right minus Y one equals to slow time X minus excellent in this case Lopez mm is nothing but why two minus Y one? Which is what I told my next where I went up on extra minus Excellent. In this case it is five minus seven upon to -4. So this -2 upon -2 which is one. And for the and the question now we can write us why minus? Why are you going to ask one? Because to slope one time x minus X one S so the Y one is seven X one is what simply why my why can't we witness x minus four plus seven? Which is why it was two X plus three. Yeah. Hard line cd. You can similarly. Right. Mhm. Why minus y. One equals two X minus X. One. Yeah. The slope will be 1 -3 upon -1 -1. 1 -3 upon -1- of one which is minus two upon minus two Which is again one. So line he's just y minus three. Upon Slope is one X minus one. The lining just wife was two x plus two. So this both our equation this is the equation of line maybe. Mhm. This is line City so we can see it. So since lope is equal. Mhm. This employee lines up you can clearly see lines up. Mhm.

Okay, There are actually four questions on this one. And the question is this given a pet of length and the question is all these lines parallel or perpendicular or neither. Which one is it? Okay, The first set off length forgiveness s the home the home Three explanations for why equals 12 three x minus. All right, bye equals well. And the other Linus four x minus three way equal. Strong. Now it might be very tempting, toe. Look at these numbers these corporations and say, Hey, this just got to be one of these parallel or properly. That's that's the temptation. But believe caresses that impatient and carefully. Uh, and that is it. The four b jump to that conclusion. Some of what time you might be become very good in being a guest. Eyeball the equation and picking up the open and so one. But I think it's better toe go through the exercise patiently in this case, what is a slowpoke lane? The American thing to understand that this is we know the slope. The question of the line is why was a mix less may And in this home, when an equation of Linus that of in this manner than M is too slow. You know this, right? So it's essential. It's very important, critical to note that that the question has to be reduced or converted to this form y equals MX, plus B importantly, being that the coefficient of why is one so unlike in this case? But we have in this case the cookie sheet is four for the 1st 1 and three in the second. So the first job will be to convert both of these two this form and then find out m one the slope for each of these and then and then did them in the for this parallel or perpendicular or neither. So you look at this one. Let's do this. Let's go ahead and convert this you. This form is now. I was separated white on one side, But let's actually hey, come on, let's take a 1st 1 the x minus, or by equal to well. And I would write the enlist the second technique patient here. So tonight Jordan, this form it will be, let's make it the stick. Me, Really? This is or why equals three X minus. Well, I don't want there but they still have to make the coefficient one. And so to do that, we divide by four on both sides to get why equals three by four Thanks, minus 12 divided before list. And so now you can say we can declare that slope. But this guy is this factor here. Three factor of X or the core patient of X, which is 3/4 fender in this accident. The over four. Thank you, no back. Let's call this. Let's call this m one because this equation like equation one, I think that this is equation on. And this is a question, too. That's called M one in one sequence. Fearful. Now that's the same thing for over on this site. Look at the second equation. It is four x minus. The way was 12. This is equation to four X minus three y equals well again. We want waken. Some experts be for me so let's it'll be why over Well, really This is three y equals or a minus Well, fuller why equals for over three x when you divide by three on both sides, the y equals four but the X minus 12 development three years for. So now you have this case you're Slope and to is this time here, or they were by three. And so now we have the two slopes. They're very different. They're not. They're not. Just the coefficient of experts will be three this case and full is no. It is actually over foreign for over a week. Okay, Now, let's have we have these two numbers now, and we know that. No, we have to make the call if I am one. And the M one equals empty would mean that panel and M one won't depart. The M two equals minus one. That would mean they are and equal. Okay, animus neither of these. Then it's just neither and less. If you look at the state before for about three, they're not equal. So they're not battle. I did not paddler. And it's in one time. Seem to equal to minus one. You look at it. It is. They were four times carefully Do it for about three equals plus one. Okay, that's not minus one. It's not profitable. What an SOS answer for a is the lines are neither perpendicular nor pattern, and you can block them out, too. Verify this, and that's what the second part of the second set of lines is. Why equals five X minus 16? So why equals five time five X minus 16 and a professional one and a second Oneness y y equals five x plus two. Secondly, questions. Why equals my mix plus two. And now this is already in the foam. They're all in the home by calls them X plus B. There was only toe convert Or do any testing because eyeball the equation and find out and say that Slow off first equation M one. This simply okay, less why and the slope off. I should use the inverse colors anyway. AM two is also plus file. So we have a case where m one equals M two. That makes these two lines, Madeleine. Okay, both What about a B C? No. I want to see five x minus six. Y equals 25. I'm going post minus five X minus six. Why, what's 25? And the second equation is like six. Plus by why equals little six X less Why? Why equals zero? Okay, all right. That's the same thing inside of the color. All right, let's let's call this equation one once a question, too. So let's take 15 x minus six. Why equals 25 between six y equals five x minus 25. And therefore, why is I've divided by six sex when you do, I bet 600 Get this So we can say. Therefore, we can say that everyone. I'm here complaining that Interpol is 5/6. Okay, now let's move to Secondly, Britain does that. Let's consider that 66 unless by why equal to zero. You know, processed religion, sex, zeros satisfies equation. But they're not here for that. Well, that's converted into the like winds and make us be forms with 58 was minus 66 or why equals minus 6/5 X. So therefore, or m two equals on a 60. Let it by five. Now let's see. Eman is not equal time too, so they're not parallel. But what about everyone dot empty. It'll m one dot him too. And one times in two equals 5/6 times minus 6/5, which is indeed minus one. Therefore, our conclusion is the lines are for pending. Why don't it's born to, uh de ah days. Why equals minus two or three X minus one? Well, it will minus two by three X minus one and second Linus. Why? Ike was three by two x minutes. Plainness. Why? Sequence three by two x minus one. Okay, this should be that easy because they already are in the y equals in X plus b fashion. So this tells us that out here I am one equals minus 21 but And this here tells us m two equals three by two. Now, you know they're not the same, but they're not problem. But how about m one dot I am too. And one times them to gives us minus two y three times two by two once a minus one. Well, it means they are perpendicular. No, there. This that these prophetically we have to That's perpendicular. See? Spoken it could these political these parallel here and the 1st 1 was neither. Balanoff clinic great to practice parties equation and finally appears over pickle

Were given. He points on a line and were asked in part a to find the equation of the line through the given point. In parallel to the given line, the equation of the given line is X minus four equals zero. In the equation of the point, this is three negative, too. It's just to make the point now, to find the equation of the line parallel to the given line. The first want to find the slope of the parallel line. This is the same as the slope of the given line. Now notice that the given line, written in the Form X equals four, recognize that in this form Slope M is undefined and therefore the slope of our parallel line is also undefined. Therefore, it follows that are parallel line is also a perform. X equals B for some constant beat. Notice that the 0.3 negative two lies in this line, so substitution give us that are three x coordinate three is equal to be and therefore plugging back in. We get X equals three. This is the equation for de line parallel to our given line in passing through the given point in part B where has to find a line passing through the given point and perpendicular to the given line? Well, ordinarily, what we would do is we would calculate the slope of the new line as three negative reciprocal of the given mind. However, we saw, the slope of the given line is undefined, so we can't do this in this case. But let's take a different approach. Now we know geometrically that are given line is a vertical line. X equals four. Therefore, in order to be perpendicular to a vertical line, our new line must be horizontal. For a line to be horizontal, it follows that our slope must be equal to zero. And in fact you can check that if a slope of our new line is equal to zero than the negative. Reciprocal of our slope of our new line is undefined, which is the same, so to speak, value of our original line. So we have the slope of our new line and equal zero, and we have a point on it. So let's use point Slope form to find the equation. How we have that? Why minus the y coordinate Negative too. Over X minus the X coordinate three equals R Slope zero solving for Why we get that. Why equals negative, too. And so this is the equation of the line passing through the given point in perpendicular to the given line.


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