Question

Write the equation of the line perpendicular to y=2/3x - 3, that passes through the point (-4,-6)

Answer 1

`y=-(3)/(2)x-12`

Explanation:

Perpendicular lines have slopes which are negative reciprocals of each other. The slope of the line y=2/3x -3 is 2/3. The slope perpendicular to it is -3/2.

Using m=-3/2, substitute it and (-4,-6) into the point slope form and simplify to find the y-intercept.

`y-y_1 = m(x-x_1)\\y--6=-(3)/(2)(x--4)\\y+6=-(3)/(2)(x+4)\\y+6=-(3)/(2)x-6\\y=-(3)/(2)x-12`