Question

what is the slope of the line that passes through the points (-2, 2) and (-4, -1)? write your answer in simplest form.

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 \( (x_1, y_1)=(-2, 2) \) and \( (x_2, y_2)=(-4, -1) \).

Step3: Substitute into the formula

Substitute the values into the slope formula: \( m=\frac{-1 - 2}{-4 - (-2)} \).

Step4: Simplify the numerator and denominator

Simplify the numerator: \( -1 - 2=-3 \).
Simplify the denominator: \( -4 - (-2)=-4 + 2=-2 \).
So, \( m = \frac{-3}{-2}=\frac{3}{2} \).

Answer:

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