Question

The slope of a line is –4 and its y-intercept is (0, 4). What is the equation of the line that is perpendicular to the first line and passes through (–8, 2)?

Answer 1

I'm going to tell you about these kinds of problems. For this particular situation, you want to find out what makes a line perpendicular and how do you find it. The answer is all about SLOPE.

First, you'd want to find point slope form for the first line.

Answer 2

@Tara03 Do you remember from our other question how to put that first line into point form?

Answer 3

yeah I know we have to plug in it -4=m and slope but the perpendicular part throws me off

Answer 4

So what is the point slope form?

Answer 5

I'll guide you through the perpendicular part.

Answer 6

i just get confused with setting it up right but i know we can simplify it down so we can get it in slope point form. so cant we get rid of the 0 in (0,4) and just have 4?

Answer 7

In this situation yes, but in order for me to show you. I'll walk you through it :)

Answer 8

Point slope form of the line if m = -4 and the y intercept is (0,4) is

y-4 = -4(x-0)

The SLOPE is the key to the perpendicular. When looking for the equation of the perpendicular line, LEAVE IT in point slope form :)

Answer 9

The key in all of this for the perpendicular line is that a perpendicular line is your point slope form line except that the slope is the negative reciprocal. Do you understand what I mean by that? Like in this case of m = -4, the negative reciprocal is 1/4

Answer 10

right I have a question though this is where I get confused is when we are seeing if its perpendicular or not. can it still be perpendicular if one line is 1/4 and the other is -1/4?

Answer 11

You mean like this?