5

8) Find an equation of the line perpendicular to 𝑦 = −2𝑥 + 1 andpassing through (5,7)....

Question

8) Find an equation of the line perpendicular to 𝑦 = −2𝑥 + 1 andpassing through (5,7).

8) Find an equation of the line perpendicular to 𝑦 = −2𝑥 + 1 and passing through (5,7).



Answers

Find an equation of each line. See Example 7 .
Perpendicular to $y=5,$ through $(1,2)$

We're finding the equation of the line that is perpendicular to X equal seven and goes through the point negative 50 So let's picture X equal seven X equal. Seven is a vertical line. That group goes through every point with an X coordinate of seven. And if a line is perpendicular to it than that line is going to be a horizontal line. So through the point negative 50 the horizontal line would be just the X axis. And that line has the equation. Why equal zero?

So house alive. We need to know is perpendicular to the lion. Why you go so minus two and we can see from this craft why you goes from minus two was here. So the land we need to know and panic alert to this lion in the house who actually caused to minors fire. So is here.

All right. Problem 62. Find the parallel and perpendicular lines that asked through the 0.56 Make it 1/2. Um, that a girl perpendicular to the line. Seven experts for Wei was eight. All right, so the first thing I want to do here is to find the slope of this equation, right? Because parallel lines have same slope and perfect power lines have Officer Cipel's and slopes, and so we need to find out. So So we're gonna solve this for why? And the what? So start by subtracting seven extra both sides. Okay, we're getting for why equals negative seven x Let's eat mended by those four, and we get why equals negative seven force ants plus two. Okay, so my parallel line is gonna have the same slow pulls. This and particular line is gonna be the opposite. All right, so, um, you know, this got fractions in it. It's still used points one slope, no form in order to get an equation, but apparently a lot. So let's just do Why minus make it 1/2 equals the slope. Maybe something worse. Minus six. Now, technically, this is the equation of line. Um I got you a little bit of algebra manipulate. This isn't something. Why, plus 1/2 equals and then distribute warms X And plus any five tweet wars. Um, many times. And negative. Positive sentence. Spot five system for, um, subject 1/2 on both sides. 1/2 in terms of 24 speed, minus 12 words. And so end up getting the equation to be. Why equals negative Seven words acts and then 35 miles 12 is 23. So plus 20 it's before this be my hair. Lola's okay. Now for perpendicular, I'm gonna do the same thing. All right? Only this time I want to, um, switched the the slope to his opposite. Reciprocal? Some? Yes. Negative to positive. And a minute switching from 7 11 44 over seven. Still gonna use, uh, stupid of these points. Look, So I get why minus Make it 1/2. He waas positive for over seven times. Necks minus six. All right, So this becomes why plus 1/2 peoples were seventh x and then you taking over here also both so negative. Four times five his name. 20 20 over or two. Right, um, and starts upstarts attract half on both sides now, um, 1/2 written in terms of 40 seconds of 21 over 42. I was 21. 012 Um, that is giving me why equals 4/7 X. Um negative. 20 minus 21 is minus 41 over two. And so this cancer, or why?

Okay. So to find the parallel line, we need to find our slope of this equation first. So it's rewrite that as three. Why is because five acts for dreams. That why you got five over three acts. So I spoke with 500. And now that he's points before we have formed were y minus Why one end? Which five? Over three. I find it to your report. So this is our parallel line equation. Now, for part B, do you want are perpendicular line? So we're just gonna flip are slope and take the negative of it. So are Slope is now negative. Feel replies with the points. Three over four comma. Oh, great. Okay, Now you have a point, but form we have y minus one. We could em which they deliver five time I minded x one just before


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