Question

a line contains the points $(-2, -2)$ and $(4, 2)$.
what is the slope of the line?

Explanation:

Step1: Recall slope formula

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

Step2: Identify the points

Let \( (x_1, y_1) = (-2, -2) \) and \( (x_2, y_2) = (4, 2) \).

Step3: Substitute into the formula

Substitute the values into the slope formula: \( m = \frac{2 - (-2)}{4 - (-2)} \).

Step4: Simplify the numerator and denominator

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

Step5: Reduce the fraction

Simplify \( \frac{4}{6} \) to \( \frac{2}{3} \).

Answer:

\(\frac{2}{3}\)