Question

what is the slope of this line? the graph shows a coordinate plane with a line passing through the points (-2, 1) and (2, 7).

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 the points

We have two points: \( (-2, 1) \) (so \( x_1=-2, y_1 = 1 \)) and \( (2, 7) \) (so \( x_2=2, y_2 = 7 \)).

Step3: Substitute into formula

Substitute the values into the slope formula: \( m=\frac{7 - 1}{2 - (-2)} \).

Step4: Simplify the expression

First, calculate the numerator: \( 7 - 1=6 \). Then, calculate the denominator: \( 2 - (-2)=2 + 2 = 4 \). So \( m=\frac{6}{4}=\frac{3}{2} \).

Answer:

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