Question

Find an equation for the line that passes through the point (-3,7) and is perpendicular to 3x-5y=80. Give your answer in point-slope form. Show as much work as possible to support your answer.

Answer 1

y-7=-(5/3)(x+3)

Explanation:

step 1

Find the slope of the line that is perpendicular to 3x-5y=80

we have

3x-5y=80

5y=3x-80

y=(3/5)x-16

The slope of the given line is m1=3/5

Remember that

If two lines are perpendicular, then the product of their slopes is equal to -1

so

m1*m2=-1

Find m2

(3/5)*m2=-1

m2=-5/3

step 2

Find the equation of the line into point slope form

y-y1=m(x-x1)

we have

m=-5/3

point (-3,7)

substitute

y-7=-(5/3)(x+3) ----> equation of the line into point slope form