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In each case determine so Ihat the line parallel to the line Sx - 2y + 36 = 0.(a)y=kx+2(b) x=ky + 2(a) What value of k will make y = kx + 2 parallel to Sx = 2y + 36...

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In each case determine so Ihat the line parallel to the line Sx - 2y + 36 = 0.(a)y=kx+2(b) x=ky + 2(a) What value of k will make y = kx + 2 parallel to Sx = 2y + 36 = 0?(Simplify your answer: Type an integer or fraction: )(b) What value of k will make x =ky + 2 parallel to Sx - Zy + 36 = 0?k=M| (Simplify your answer: Type an intoger or fraction: )Enter your answer in each of the answer boxesType here to searchRi

In each case determine so Ihat the line parallel to the line Sx - 2y + 36 = 0. (a)y=kx+2 (b) x=ky + 2 (a) What value of k will make y = kx + 2 parallel to Sx = 2y + 36 = 0? (Simplify your answer: Type an integer or fraction: ) (b) What value of k will make x =ky + 2 parallel to Sx - Zy + 36 = 0? k=M| (Simplify your answer: Type an intoger or fraction: ) Enter your answer in each of the answer boxes Type here to search Ri



Answers

Find $k$ if the lines $4 x-k y=6$ and $6 x+3 y+2=0$ are parallel.

This question asked us to determine for which values of K or the two lines parallel and perpendicular. So part is parallel. What we know is that we're writing the two lines and slope intercept form. This is equivalent to a wise negative to over K times acts puts three over ke the K essentially part of the coefficient or the slope. What this means is that for two lines to be parallel, they must have the same slope. Therefore, negative to over K must be equivalent to negative one. Therefore, K must be too. So the answer parties case too. Now perpendicular slopes we can get from parallel slopes if we have Kay is too. We're looking at the negative, reciprocal or in other words, the perpendicular would have to be negative. Given the reciprocal we know we simply attach a negative sign on. So we have Kay is negative

This problem wants you to find the X coordinate K. In the coordinate K. Two and four negative one for each of the following lines. So parallel to three, Y plus two, X is equal to six. So we gotta find the slope of that line. So I'm going to write this in Y intercept slope intercept form. So let's subtract two X from both sides. You get three, Y is equal to negative two X-plus six, divide both sides by three and you get Y is equal to negative two thirds X plus two. So our slope is negative two thirds because it's parallel, there'll be this time that we're looking for has the same slope. So let's set this up as well. Set this up as Y two X 2. Why one x 1 And put in our slope value here of negative 2/3 must be equal to Y two to minus y one, negative one over Next to K -X one, which is four. And we got to end up solving for K. here. So what we'll get when we simplify this is negative 2/3 is equal to three over K -K -4. So what we can do is reduce those three down essentially. Well let's cross multiply actually here, so we'll get negative two times. K -4 is equal to nine equal to nine when you multiply across. And let's solve for K. And I'm going to have to do this up here. So we'll solve her case. We get negative two K plus eight is equal to nine. subtract 8 from both sides and you get negative two K. Is equal to one, divide both sides by negative two. And you get a K. Value of negative one half for that point? For part A for part B. We're gonna do the same thing. I'll just have to write a little bit smaller here. So let's get why by itself will add five X. To both sides. And we got to y is equal to five X plus one. The bible sides by two. And you get y is equal to 5/2 X plus one. Now perpendicular means the slope is going to be the inverse and opposite. So negative 2/5 which will be equal to. Again, our coordinates set up the same way as lax it's time. So to minus negative one over k minus four. So let's cross multiply right away. I'm going to make this just so that we know that equals three. So we get negative two times K minus four is equal to 15. And let's solve for K. So I'll solve for K by distributing the negative two and so we get negative two. K plus eight is equal to 15. Subtract eight from both sides. We get negative two. K is equal to seven, divide both sides by negative two, and we get our K value Equal to 7/-2 Or negative three points.

And welcome to this lesson in this lesson. We have two lines. Two x plus K. Y is a quote to then we have four x plus. Why is he caught one? And we've been required to find the value off K that makes their two lines the first line in the second line in particular. Yeah, so for them to be in particular the slope, they should haven't a negative where Cipro cars look. That means that when you multiply the two slopes, you should get negative one. So let's right all of the questions with why, as the subject. So for the first one we have que y is he called to minus two x for purposes off. This would write the X fest. Uh huh. And dividing by key gives us why is he called to negative two k x last too. And also the second. So this is the modified fast. The second one is four x mine blast. Why is it called one if you send four X to join the one? Okay, so this becomes the modified equation too. So for want off clarity, let's put the to modify the cushion side by side And this is why is he called to Negative four X plus one? You would identify the slope as the coefficient off the X. So for pamper and vehicular for him in the clarity, we have the slope of the first one times the look of the second one should give us negative one. If you multiply them, should give us a negative one. So what is the value that would make the host and negative one? Okay, so this is so for the purposes off the first one, it's only multiply that you have eight Cuba K is recalled to negative one. So this implies Dad aids Google minus one is he called two K when you do cost much application, and K is he call to negative age. So for the two lines to be perpendicular, case should be caught Negative eight. Okay, so the answer is one that is key. If you go to negative eight for the two lines again to be parallel, it means that they should have the same slope. That means that negative Whoa! Oh, means that the slope, right two okay, should be equal to negative four. All right. And that's just equal to the group of the Fast should be called to the slope of the second. And when you do cross multiplication, you have negative. So this implies that negative to Chicago to negative four k divide by negative four. You were by negative four. So this course is out that then it means that we have negative two negative force equal to K and K is equal to half. So it means that the second bad K is equal to have for the two lines to be parallel. For them to be from particular, K would have to be called to negative eight. Thanks for a time.

Okay, so this problem has two parts. The first is to find if you were okay, such that the line that passes through these two points is parallel to the line described by desecration. So to do that, we're first going to find out the slope of this line. Oh, and to do that, working a rewrite, this equation in the slope intercept form. So the person you want to do is get white by the term required by itself on this side of the equation and which means this guy needs to go over here and the first out jigga. Then we're going to do so. We're going to subtract two X from here, and that means we're gonna have to do the same thing over here. So this first step gets this on this side thes to cancel out. So we're left with three. Why? And on this side and half months to x six. Okay, so the next thing that we wanted to is to have wise the coefficient for wife to be working to do that, we're going to deny it this side by three, so the coefficient can be won. But since we didn't know this. Maybe you need to do it on this other side. So here, like, we want to please cancel out to one. So why is left with courage? Efficient one. Here we have distributes, though this side gets I mean, the first term is minus two over three X on DH six over three two. So this is the no intercept form thehe creation on, which means that we have found out still desecration. That's the coefficient of X here. And let's call it one. Kiss its fruit with this wind, not vote, not the line that passes through these two points. This and it's going to be minus two over three. Okay, so since peace aligned that passes will be face to points. We wanted to be parallel to this. That means that the end that we're looking for it's also going to be what I am one so thiss iss the slope that we want between these two months. So now we're gonna use the definition of Slope Teo to find the relationship between these numbers and this number that we just felt. So if we remember definition of slow, it is the differences in, um, the white ordinance. That would be why two minus one minus a negative one over. The difference is in the X coordinates. This case will have K and four. Yeah, And this We found that we wanted it to be negative to over three. Okay, so we cannot do without this. Let's take care of this. Double negatives. So, on one side of the equation, we're going to have Linus to over three. And on the other side, we're gonna hop two last one. These two negatives become a plus sign. So we have three. And since we don't know Okay, yes, we leave. This s dance. Okay. Is what So we want to find a no about me for K that satisfies desecration. So to do this, we're gonna cross multiply. Oh, so three s history is gonna be over here and K minus park. Just gonna go over here b to simply have came in this for times. Take it up to two times. Three times three. Okay, so now we can go ahead and distribute this too. Wei have minus two K and negatives. Two negatives become possible. We're a multi playing here, and I wrote a play here again his name King. So since we want to find out who Kay? Yes. Let's look at this guy over here by subtracting it from here and from here. Um, Sunder said we're left. Quit two k. And what? And because again, we still haven't. Okay, we aren't going to designed by minus two on the sets and these two to cancel out. And we have that K iss. Uh, I'm gonna write this negative. Put it up here. It should be the same. So this is the value for cake if we want the line that passes through these two points to be parallel to the equation described by this line. So part two working a deal with the same, you know, the same points. So, uh, first point is going to be for and minus one, and second point is going to be a mysterious K on DH two. We want to find a value for Kane such that the line that passes through these two points is now perpendicular to decline. Described by this equation five X minus two. Why he quotes to what? Okay, so we're going to do the same approach as we did hear uh, first we're gonna find Go slope for it. This line. Yeah, to do that, we're gonna be right it as a We're going to relate it in the soup intercept form. So that means first we have to turn with y two b by itself here, and we're going to move this guy over here, so should be negative Underside and the world will remain positive. So, um, two next step is we wanted coefficient for y to be one right now. It's native to sewer. Gonna multiply and divide this by next to, and we need to do the same on this side. All right. So used to cancel out to one. And we have the why would coefficient one as we wanted. And this negative too will distribute here. Thes two negatives. Look up to be positive. Mmm. Cut like over two times. X minus one over two. So now this is the slope intercept form, which means that we have found them one, which is the slope for this mine. It's five over two. So now we want to find out who m iss. Um and it's what we're calling the slope for the line that passes through these two points. So since we want to be to have this line be perpendicular to this, that means that if we multiply and won bye em it should be negative one. So we since we know someone else we're gonna plug that in for this and it's who were looking for. And that one stays the same. Sit to figure out her, Imus, We're gonna multiply, decide, but to over five. Which means we need to do the same thing you decide. And here, this cancels with this and we have an equals. We're gonna put this negative. Same with, too. When is too over. Right? No, uh, how this this number relate to these numbers over here. So we're gonna use like we did here. The definition of slope. So Slope iss The difference in why Croydon It's here divided by the difference in the X coordinates. Silk. Don't top heard. Um, why coordinate a second point minus? Well, like ordinate of the first point and the top. We have ex Corde in it at the second point, Mennis, excluding it of the first point. So like we did before, we're going to get rid of these double negatives here. And since we have two plus one gonna write three here. And since we still don't know hope ks were just gonna write Cape New minus four. Okay, so now we're going Tio, cross multiply. Um, that's going to give us minus two times came minus four and five times. Hey, no, we can simplify, but this pretty simplified this pride. We're gonna distribute the minus two soon minus two tests. Okay. And minus two times four Quinn to give us on the other side. We have fifteen. No, we want to pass this guy over here, so we're gonna subtract age from here, which means we're gonna have to do the same on this site. So here we have minus two king. And on the other side, fifteen minus eight, we have seven. And to find out who kay s or going to denied by this cool efficient here, Which means you're also gonna have to do the same underside on, please to cancel out. And we have King to be men's seven over two. So this is the value of for Kate, then makes the line that passes through these two points perpendicular to the line described by this equation.


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