Question

A line that perpendicular to the line y= 2/3x + 4 and goes through the point (-2,5)

Answer 1

step 1

Find the slope of the given line

we have

y=(2/3)x+4

the slope is m=2/3

Remember that

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

so

the slope of the perpendicular line to the given line is

m=-3/2

step 2

Find the equation of the line in slope intercept form

y=mx+b

we have

m=-3/2

point (-2,5)

substitute

5=(-3/2)(-2)+b

solve for b

5=3+b

b=2

therefore

y=-(3/2)x+2