Question

Find and equation in slope-intercept form, of the line passing through (5,-2) and (-8,3)

Answer 1

`y =- (5)/(13)x - (1)/(13)`

Explanation:

First, calculate the slope using the slope formula and the two points given.

`m = (y_2-y_1)/(x_2-x_1)= (3--2)/(-8-5) =-(5)/(13)`

Write the equation of the line using m = -5/13 and the point (5,-2) into the point slope form. Then simplify into the slope intercept form.

`y - y_1=m(x-x_1)\\y - -2 = -(5)/(13)(x-5)\\y+2 =- (5)/(13)x +(25)/(13)\\y =- (5)/(13)x - (1)/(13)`