Question

Write an equation that passes through the given point and that is perpendicular to the given line in slope intercept form (-2,-4), y=-2/7x+1

Answer 1

Perpendicular lines have slopes that are negative reciprocals. That means that when you multiply together the slopes of perpendicular lines you get -1. In a practical way, if you have the slope of a line and want the slope of a perpendicular, write the slope as a fraction, then flip the fraction, then change the sign.

Answer 2

First let's find the slope of the given line:
y = -(2/7)x + 1
Since this equation is already written in y = mx + b form, we can read the slope directly.
m = -2/7

Answer 3

ok thanks so then what if the slope was already was negative,will that mean that the slope will turn into positive?

Answer 4

Correct.
Now we figure out the slope of a perpendicular to this line:
m1 = -2/7; m2 = 7/2

Answer 5

We flip the fraction and change sign. The slope of the perpendicular is 7/2.
Now our question is what is the equation of the line that has slope 7/2 and passes through (-2, -4)?

Answer 6

You can use the slope-intercept equation,
y = mx + b,
let m = 7/2, x = -2, and y = -4, and solve for b

Answer 7

Yes so then when we plug in the X and Y of the given points it will be 4=7/2(-2)+b

Answer 8

Negative 4, not positive 4

Answer 9

Oh yes my bad.the slope will be b=3 ?

Answer 10

yes

Answer 11

So then the new intercept form will be y=7/2x+3

Answer 12

Correct

Answer 13

So then the only thing different than the parallel line equations is changing the slope into a reciprocal form right?

Answer 14

Right. Figuring out the new slope is different, but then getting the equation is the same procedure.

Answer 15

Can you help me in another problem in another post please?