In Exercises 1–4, write an equation for line L in point-slope for...

Question

In Exercises 1–4, write an equation for line L in point-slope form and slope-intercept form.

Graph showing line L in red, perpendicular to the blue line with equation y = (x/2, -2).

Accepted Answer

Use the slope intercept form and slope form to write the equation of the line shown. Looking for a line L which is the blue line. Now to find el we need a couple of things. We need a point anywhere on the line and the slope of the line. Now we don't know if the slope is just yet, but we can find it. This crucial piece of information here says ellis perpendicular to our other graph, Y equals X over two minus two. If two lines are perpendicular, there are two slopes and one times M two should be equal to negative one. We can rewrite this to find what R. M wants to be. So we'll see M1 is the slope of line L. You know M two is the slope of our second line. It says X number two, that is one half equals negative one. Now we divide those sides by 1/2. This gives us M1 equals -2. So the slope of our line is -2. Now we can use point slope form to make a line point slope form is given by y minus Y. One equals M times x minus x one. Where Y one X 1 is a point on our line Sauce X one, Y 1. We want to point on our graph. L. We notice here we can use 00. So I'll use 00 as our point. Now I will write our point slope form. We have y last Y120. You have an M. Which we said was native to two times x zero. This will give us our points of form. Now I want to find slope intercept form. We know slope intercept form is given by Y equals M X plus B. The slope except all. Right out here. Point slope what In the form Y equals mx plus B. You notice here though we have zeros in there, we can go ahead and remove those zeros, get Y equals negative two times X, which is in slope intercept form. So the answer to our problem are y minus zero equals data, two times X minus zero and Y equals negative two X. If we look at the possible answers, the answer to this problem turns out to be answer D. Okay, I hope to help you solve the problem. Thank you for watching. Goodbye.

In Exercises 1–4, write an equation for line L in point-slope form and slope-intercept form.

Key Concepts

Point-Slope Form

Slope-Intercept Form

Perpendicular Lines

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