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Consider the following Point Line (8 7* + 3y - (0) Write an equation of the Ilne passing through the given point that is parallel t0 the given Ilne.(b) Write an equ...

Question

Consider the following Point Line (8 7* + 3y - (0) Write an equation of the Ilne passing through the given point that is parallel t0 the given Ilne.(b) Write an equation of the Ilne passing through the givan point that perpendicular to the given Ilne,

Consider the following Point Line (8 7* + 3y - (0) Write an equation of the Ilne passing through the given point that is parallel t0 the given Ilne. (b) Write an equation of the Ilne passing through the givan point that perpendicular to the given Ilne,



Answers

Finding Parallel and Perpendicular,
write equations of the lines through the given point (a) parallel to and (b) perpendicular to the given line.
$$x+y=7, \quad(-3,2)$$

Were given a point in a line and were asked, in part a to write the equation of the line. Through this given point parallel to the given line, the line has the general equation three X Plus four y equals seven, and the points were given is negative two thirds 7/8. So to find the equation of the line parallel to our given line, let's find the slope of the given line to do this well, right. The equation in slope intercept form. So we have four y equals negative three x plus seven and therefore that why is equal to negative 3/4 x plus 7/4. From this, we see that the slope of our old line and therefore our new lines. The new line is parallel to the old line. This is negative 3/4. Now we have the slope of our new line, negative 3/4 and the point on the line, so we'll use Point Slope form to write the equation of the new line. We have y minus the y. Coordinate 7/8 over X minus The X coordinate negative two thirds equals negative 3/4 Solving for Why let's cross multiply so we have once I actually crossed my boy, multiplying both sides by X plus two thirds we get why minus 7/8 equals negative 3/4 times X and then we have minus 3/4 times. Two thirds is 2/4 or one half. Solving for Y. Why is equal to negative 3/4 x and then we have negative one half plus 7/8 or 4/8 negative 4/8 plus seventies. So plus 3/8. So this is the equation of the line perpendicular to are given.

Were given a point in a line and in part a were asked to write the equation of the line through this point. In parallel to the given line, the line is equation five X plus three y equals zero, and the point on the line is 7/8 3 4th now. As I said in part, they were looking for the wine parallel to the given line in order to do this. That's right, our line in slope intercept form So we have Y is equal to negative five X, but then divide by three. So it's negative five thirds x. From this, we see that the slope of our original line is negative five thirds, and therefore, the slope of our new line, which is parallel to the original line, is also negative. Five thirds. Now we have the slope of the new line and a point on it, so we'll use Point Slope form to write the equation of this line. So we have Y minus the y. Coordinate 3/4 over X minus. The X coordinate 7/8 equals slope negative five thirds solving for why have y minus 3/4 equals negative five thirds x plus, then we have 7/8 times five thirds is 35 24th. Solving for y y equals negative five thirds x plus 35 24th plus 3/4. This is the same as plus 18 24th, so we have 35 plus 18 is 53 24th. And so this is the equation of the line through the given point in parallel to our given line that in part B, we want to find the equation of the line through the given point and perpendicular to the given line. To do this, we want to find the slope of the given of the new line. We know the slope of the new line is going to be the negative reciprocal of the slope of the Given mine, which we found was negative five thirds. So flipping and multiplying the denominator, we get 3/5. This is the slope of our new line. We have the slope of the new line and a point on the new line, so we'll use point slope form. That's right, the equation of the new line. Yeah, so this tells us why. Minus the y coordinate 3/4 over x minus The X coordinate 7/8 equals the slope 3/5 Southern for why we have. Why minus 3/4 equals 3/5 x minus 21 40th So that why is equal to 3/5 x minus 21 40th plus 3/4 their words minus 21 40th plus 70th We're plus nine Fortius. So this is the equation of the line perpendicular to the given line in passing through the given point.

The discussion will record that, given the two e questions on the and one will be Why equal to yeah, why in coaching the, um, one X and then plus B one on the Nhu. Why, you could, um, to express with you? And we know that that one but allows you the m chu even only if I am one equal to the M two and one perpendicular to the event you even only if I am one times m two equal to minus one in this question, here were given the point. You go to the minus 32 and we have the question on the line X plus. Why a country seven Not to stand from this equation. Here, you can ride a why? Because you want X minus one X plus seven. So the slump in this equation will be a micoach minus one. And in the part, I am the question. We want to find the question on the line going through the pond here on then, but allowed you this line so by Latino one equal, tremendous one X plus seven and therefore here using this one, we have the slump almost equal to the minus one, And then we can get the why equal to minus X plus B to find a B here. We know that extra two minus three. Why would you chew? Were black into here to get the two equal Children, Uh, minus minus three plus B. They're found to be most equal. Do No. Five. And from here you can get the question under Why must decode you the minus X plus five. So this will be the answer for the part A. Or we can write us an ingenuous standard form. Be, uh minus X plus y minus. Plus five You go to I'm sorry. This one will be the minus. X manners y plus five equals zero Now for the bad day. Once you have the perpendicular to the Y equal to minus one X plus seven. From here we can find the slump. EMAS eco to the one and then we have the question would be Why ico thio x plus b again this in this point here we can to equal to the minus three plus B and found a B must equal to the five be equal to the five here and I think this was a big mistake here. This will not equal to five. It will be three to minus three equals U minus one. So this will be the minus one here. And then the answer for Alison will be, um, minus one. We can write this down to the X plus y. Plus one in coach is zero. And the answer for this one will be the Y ico tuned the X plus five. Uh, it will be X minus quite plus five equal to zero.

In this question will record that, given the two e question the line and one why equal to the M one X plus B one and you? Why equal to m two X plus b two We say anyone but I loved you. The l two even on if the m one equal to the M two and one perpendicular to the l do it only if m one times m two u h minus one in this question were given the pond you go junior three out of 47 out of eight and we have the line here will be five x ministry. Why equal to zero? Understand this question? We can write it down into the why equal to the 503 X and they found a slob. I am equal to the 503 here and in the part. I want to find the equation The line going through the point here and but allowed to this line. So we have that allowed you know why? Including the 503 x From here, we can get the Islam we're looking from. We included the fight of three as well. Therefore, we have the Why equal to find out of three X plus B. Now, to find this be here, notice that we have the action and why Now we're looking and Uganda seven out of eight ego to five out of three times three out of four plus B doesn't oblige them. Famous equal to 708. My nurse, this one will be three cans. Allow five out of four, then we can equal to minus five out of four. So when you go to the monastery under eight as a result again, the answer will be why he go to five out of three ex on, then minus three out of eight. We can rewrite 308. We can multiply everything with the 24. So we shouldn't get now will be the 24. Why equal to the for equal to the eight times five will be 40 X. Why not this one going to be in the three times three will be minus nine. We can write this down to the fourth e x minus 24 Y minus 90 Coaches zero. There's gonna be the answer for the part. I now for the puppy we want to have a perpendicular to the one equal to five out of three ex. From here we can get the slump. Embassy coach, Ministry under five Therefore, we have the one must go to ministry. Enter five X. Let's be Do you find a Be here again This in this point. Now we will have the 708 equal to ministry under five times in the three and four plus b. Therefore, the B must equal to 708 plus Then I out of 20. Then we get equal to seven out of eight and then plus then I went up 20 So we get equal to the fifty three hundred four day from here We Ghenda, Why must ego Jew on the street until five x plus 53 under four day? We can want to play everything with the 40 And then we have the 40 y equal to hear the minus 24 x plus 53 Or we can write this down into the form minus 24 x minus 40 Why? And then plus 53 he coaches zero and this could be the answer for the part pay


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