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Point) Line k has the equatlon y = ~4x + 2.Line € Is parallel to Ilne k_ but passes through the point = (1,1) .Find an equation tor Ilne € in both slope...

Question

Point) Line k has the equatlon y = ~4x + 2.Line € Is parallel to Ilne k_ but passes through the point = (1,1) .Find an equation tor Ilne € in both slope-Intercept Iorm and point-slope torm using the given point.An equation for € in slope-Intercept form Is:An equation tor & In polnt-slopa torm Is:

point) Line k has the equatlon y = ~4x + 2. Line € Is parallel to Ilne k_ but passes through the point = (1,1) . Find an equation tor Ilne € in both slope-Intercept Iorm and point-slope torm using the given point. An equation for € in slope-Intercept form Is: An equation tor & In polnt-slopa torm Is:



Answers

Write in slope-intercept form the equation of the line that is parallel to the given line and passes through the given point. $$ y=2 x-11,(3,4) $$

This problem asks us for party to find a parallel line. 23 y plus two x equals six that goes through points. Negative. So sorry. Four. Negative one K two. We need to determine what K is, um, in our slope point form equation, which is I'm going to use to find out what K is K is my ex to part First, I need to know Figure out what M is the slope, and it's given parallel to this. So let's get this in, um, y equals MX plus B form. So why is going to equal negative two x plus six by subtracting two extra both sides divided by three to get why by itself you get y equals negative two thirds X plus two. That means our M value is right here. It's negative. Two thirds so negative two thirds x two is K minus. X one is four equals y tu minus y one. So two minus negative one. So let's simplify a few things here. So what I can do is go to minus negative. One is three equals. Distribute that negative two thirds. What's negative? Two thirds to the K and negative two thirds times negative fourth positive eight thirds. Instead of dealing with these fractions, I can use the trick to multiply both sides by the lowest common denominator in this case is three, so you're going to end up with nine is equal to negative. Two K plus eight. Divide AR minus eight from both sides. You get one equals negative. Two K. Divide both sides by negative two, and you get a K value of negative one half for party for Part B same coordinates, but it's looking for a line perpendicular to two y minus five X equals one. So again, same strategy. Determine the M here by getting this into y equals form so it's only two equals five x plus one by adding five X to both sides here and you'll get the viable sides by two. You get y equals 5/2 X plus one half. Now remember, it's looking for a perpendicular, um, lines, so that means they're going to have the inverse and negative of this slope. So that means M will be equal to negative two fits. So let's plug that in for em here. I'm going to work in green, so negative 2/5. And then let's start plugging some values in X two is K minus. X one of four equals two minus negative, one for Y two minus y one. So let's simplify this again. We get three is equal to negative two K over five, and that will become plus 8/5. Again. Same strategy can multiply both sides by five year. To remove the fractions, I get 15 equals negative two okay, plus eight minus eight from both sides, and I get negative. Two. K equals seven. Divide both sides by negative two and you get a K value of negative seven over to.

So for this problem, we're going to want to first look at, um, the slope of the first line. So if we solve for why, we would end up getting that the slope is a negative two thirds. So that's the main slope we want to focus on. Um and then, if it's in normal form, will have y equals a negative two thirds X plus b. Um, and we want to plug in a four negative one there because that's one of the points that we have. So we'll put in, um are negative one right here. I'll put in our four right there. Then we solve for B and we end up getting, um, this will be a negative eight thirds. So plus 3/3, Um, plus a negative 3/3. Well, give us a five thirds, so b equals five thirds. So we have y equals a negative two thirds X plus. I have over three. Um, and we know that, too, is a y value. Um, and we want to see what K equals at that point. And here we see, it's a negative one half so negative. One half is r k value for that. And then for part B, we want to see, um, slope intercept form. Um, so what we'll have is again, we want to determine the slope. It'll be five halves in this case or 2.5. So we have, um Why equals five halves X plus B. And we know we can put a point through, um, for negative one again. So it will be our negative one. And this will be for when we do this, we know that these would cancel. Um, we would get 10, and then we would subtract that. So be is negative. 11. So we have y equals of five halves X minus 11 onda. We want to see what's happening when K is equal to two or when y is equal to two and we see that occurs right here. And at that point, K equals 5.2. Or that's one of the values that we could have so that would end up being our answer for this particular problem.

Okay, so we want to find their came about. You're given a slope, and that's actually equal to carry. And two points. So let's take a difference of our Y values. That's one minus K minus 83 plus two K all over The difference of our X value Said it came on its one minus K plus one. So here we have 11 is king. When his three months to Okay, all over. K minus one minus k an a minus one. So that's going to give us a, um, negative to money streak a all over a negative too. So I'm gonna multiply both sides by a negative too. So we're gonna use this portion of this portion, so that's going to give us a negative to Cain is equal to negative two minus three carrying. Now let's move or K terms to our left hand side. So I'm gonna add three. Can both sides. When we get there, OK, value must be equal to a negative chip

This apartment number 469. We have been given a line Y plus six people, seven equal to zero And .1 Common -1. We need to find the question of the straight line which the paddle to this land and passing through one common -1. So we know that this is a question of a horizontal line whose slope is zero And this is the point. Excellent. Come away one. So we'll be using via minus y. One equal to m x minus. Excellent. So why are -1 equal to 0? X -1? So why plus one equal to zero? Now subtract one from both. The sides will be getting what I call to -1. They should be the required answer. Thank you.


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