Question

the graph shows a quadratic function f(x) and a line ℓ that intersects f(x) at two points. the coordinates of these points are (-6, 2) and (6, -4). what is the slope of line ℓ?

Explanation:

Step1: Recall slope formula

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

Step2: Substitute given points

Let $(x_1,y_1)=(-6,2)$ and $(x_2,y_2)=(6,-4)$.
$m=\frac{-4-2}{6-(-6)}=\frac{-6}{12}$

Step3: Simplify the fraction

$\frac{-6}{12}=-\frac{1}{2}$

Answer:

$-\frac{1}{2}$