Question

A line passes through the point (6,-1) and is perpendicular to the line with equation - 2x + 3y = -6.

Answer 1

Answer: y = − 3/2 x + 8

Step-by-step explanation:

Find the Perpendicular Line

Solve −2x + 3y = −6.

y = −2 + 2x/3

Find the slope when y = −2 + 2x/3 .

m = 2/3  

The equation of a perpendicular line must have a slope that is the negative reciprocal of the original slope.

$m$ perpendicular = $-\frac{1}{\frac{2}{3} }$

Simplify to find the slope of the perpendicular line.

perpendicular = −3/2

Find the equation of the perpendicular line using the point-slope formula.

y + 1 = − 3/2

⋅ (x − 6)

Write in y = mx + b form.  

y = − 3/2 x + 8