Write an equation that is perpendicular to 3x-5y=5 and passes through the point (9,-14)

Answer 1

They are not specifying in what form to put the answer. So I would stick with General Form Ax + By = C. For perpendicular this becomes becomes Bx - Ay = C interchanging the original A and B and changing the sign.

5x + 3y = C

Now plug in the known point (9,-14) to find C.

5(9) + 3(-14) = C

45 - 42 = C

C = 3

5x + 3y = 3

Answer 2

First you want to get the equation into slope-intercept form: 3x - 5y = 5 becomes y = 3/5 x - 1.

The slope of the line is 3/5. And the slope of the perpendicular of the line is the negative reciprocal: -5/3

So the equation for the perpendicular line is y = -5/3 x + b.

To get b, plug in the point (9, -14): -14 = -5/3 x 9 + b. So, b = 1.

The equation for the perpendicular of the line is y = -5/3 x + 1.