Question:

Using slopes, determine if the points lie on a straight line.

a) $\displaystyle (-1,-4)$ , $\displaystyle (3,8)$ & $\displaystyle (0,-1)$

b) $\displaystyle (0,5)$ , $\displaystyle (-1,3)$ & $\displaystyle (-3,2)$

Attempt:

a) $\displaystyle (-1,-4)$ & $\displaystyle (3,8)$

$\displaystyle m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{8-(-4)}{3-(-1)} = \frac{12}{4} = 3$

$\displaystyle (3,8)$ & $\displaystyle (0,-1)$

$\displaystyle m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-1-8}{0-3} = \frac{-9}{-3} = 3$

It is a straight line as the slopes are the same.

b) $\displaystyle (0,5)$ & $\displaystyle (-1,3)$

$\displaystyle m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{3-5}{-1-0} = 2$

$\displaystyle (-3,2)$ & $\displaystyle (-1,3)$

$\displaystyle m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{3-2}{(-1)-3} = \frac{1}{-4} = -\frac{1}{4}$

It is not a straight line as the slopes don't match.

are my answers correct?