Question

line m contains points a, b, and c, where a is (1, -3), b is (2, -6), and c is (-1, 3). what is the slope of line m?
a. 3
b. -\frac{1}{3}
c. \frac{1}{3}
d. undefined
e. -3

Explanation:

Step1: Recall slope - formula

The slope formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $m=\frac{y_2 - y_1}{x_2 - x_1}$.

Step2: Choose two points

Let's choose points $A(1,-3)$ and $B(2,-6)$. Here $x_1 = 1,y_1=-3,x_2 = 2,y_2=-6$.

Step3: Substitute values into formula

$m=\frac{-6-(-3)}{2 - 1}=\frac{-6 + 3}{1}=\frac{-3}{1}=-3$.
We can also check with other pairs. Let's take $A(1,-3)$ and $C(-1,3)$. Then $m=\frac{3-(-3)}{-1 - 1}=\frac{3 + 3}{-2}=\frac{6}{-2}=-3$.

Answer:

E. $-3$