Question

A line contains the point (–3, –4) and is perpendicular to a line with a slope of 3/5. Write an equation of the line satisfying the given conditions. Write the answer in slope-intercept form.

Answer 1

`y = -(5)/(3)x -9`

Explanation:

Perpendicular lines have negative reciprocal slopes. Since the slope of one line is 3/5, its perpendicular line will have the slope of -5/3.

Substitute m = -5/3 and (-3,-4) into the point slope form of a line.

`y - y_1 = m(x-x_1)\\y - -4 = (-5)/(3)(x --3)\\y + 4 = -(5)/(3)(x +3)\\y + 4 = -(5)/(3)x -5 \\ y = -(5)/(3)x -9`