Question

Find the slope of the line that passes through each pair of points. Express as a fraction in simplest form. (-6, -2), (-1.5, 5.5)

Answer 1

m = slope= 5/3

Explanation:

`(-6, -2) = (x_1,y_1) \\ (-1.5, 5.5) (x_2 ,y_2) \\ (y - y_1)/(x - x_1) = (y_2 - y_1)/(x_2 -x _1)`

`(y - ( - 2))/(x - ( - 6)) = (5.5 - ( -2 ))/( - 1.5 - ( - 6)) \\ (y + 2)/(x + 6) = (5.5 + 2)/( - 1.5 + 6)`

`(y + 2)/(x + 6) = (7.5)/(4.5) \\ 4.5(y + 2) = 7.5(x + 6)`

`4.5y + 9 = 7.5x + 45 \\ 4.5y = 7.5x + 45 - 9 \\ 4.5y = 7.5x + 36`

Divide through by 4.5

`(4.5y)/(4.5) = (7.5x)/(4.5) + (36)/(4.5) \\ y = (5)/(3) x + 8 \\`