Question

what is the slope of this line? the line passes through points (-2, 6) and (2, -2). the options are -2, $-\frac{1}{2}$, 0, undefined.

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: Identify points

We have two points: \((-2, 6)\) (so \( x_1 = -2, y_1 = 6 \)) and \((2, -2)\) (so \( x_2 = 2, y_2 = -2 \)).

Step3: Substitute into formula

Substitute the values into the slope formula: \( m = \frac{-2 - 6}{2 - (-2)} \).

Step4: Simplify numerator and denominator

Simplify numerator: \( -2 - 6 = -8 \). Simplify denominator: \( 2 - (-2) = 2 + 2 = 4 \).

Step5: Calculate slope

Now, \( m = \frac{-8}{4} = -2 \).

Answer:

\(-2\)