slope intercept form of a line that is perpendicular to

Question

Write an equation (slope Intercept Form) of a a line through (-3,-2) that is perpendicular to 2x+4y=-7

Answer 1

First we have to find the slope of 2x + 4y = -7

 

Solve for y by subtracting 2x and then dividing by 4 to get

 

y = (-7 - 2x)/4 or y = -1/2x - 7/4

 

This shows the slope as -1/2

 

The perpendicular slope is the negative reciprocal of this or 2/1 = 2

 

So the perpendicular line equation will be y = 2x + b

 

To find b plug in the given point (-3,-2) so -2 = 2(-3) + b

 

Solving for b gives b = 4

 

Now you can write the full equation y = 2x + 4