Question

What is the equation of the line in slope-intercept form that is perpendicular to the line y =3/4 x – 2 and passes through the point (–12, 10)?

Answer 1

`y=-(4)/(3)x-6`

Explanation:

Perpendicular lines have slopes which are negative reciprocals of each other. The slope of the line y=3/4x-2 is 3/4. The slope perpendicular to it is -4/3.

Using m=-4/3, substitute it and (-12,10) into the point slope form and simplify to find the y-intercept.

`y-y_1 = m(x-x_1)\\y-10=-(4)/(3)(x--12)\\y-10=-(4)/(3)(x+12)\\y-10=-(4)/(3)x-16\\y=-(4)/(3)x-6`