Question

find the slope of the line passing through the points (-2, 3) and (-6, 8).

Explanation:

Step1: Recall the 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 coordinates

Let \( (x_1, y_1)=(-2, 3) \) and \( (x_2, y_2)=(-6, 8) \).

Step3: Substitute into the formula

Substitute the values into the slope formula: \( m=\frac{8 - 3}{-6 - (-2)} \).

Step4: Simplify the numerator and denominator

Simplify the numerator: \( 8 - 3 = 5 \).
Simplify the denominator: \( -6 - (-2)=-6 + 2=-4 \).
So, \( m = \frac{5}{-4}=-\frac{5}{4} \).

Answer:

\(-\frac{5}{4}\)