Question

10. Linek is graphed below. Write an equation for line m that is perpendicular to line (there are multiple correct answers).

Answer 1

step 1

Find the equation of line k

the slope of line k is

m=-3/4 ------> previous answer

step 2

If two lines are perpendicular, then their slopes are opposite reciprocal

so

the slope of the line m must be equal to

m=4/3

I will assume a point (3,4)

Find the equation in slope intercept form

y=mx+b

we have

m=4/3

point (3,4)

substitute

4=(4/3)*(3)+b

solve for b

4=4+b

b=0

therefore

y=(4/3)x -----> equation in slope intercept form ( this line is perpendicular to line k)

Find the equation in point slope form

y-y1=m(x-x1)

we have

m=4/3

point (3,4)

substitute

y-4=(4/3)*(x-3) -----> equation in point slope form ( this line is perpendicular to line k)

Find the equation in standard form

Ax+By=C

where

A is a positive integer

B and C are integers

we have

y=(4/3)x

Multiply by 3 both sides

3y=4x

4x-3y=0 ------> equation in standard form

y=(4/3)x

y-4=(4/3)*(x-3)

4x-3y=0