Question

line m goes through points a and b. what is the slope of line m? start by writing an expression that would represent the slope of line m, or the change in vertical distance for a given change in horizontal distance. point a: (3, 2) point b: (8, 5) slope = \frac{vertical distance}{horizontal distance} = \frac{}{} change in x - values change in y - values

Explanation:

Step1: Identify slope components

Vertical distance = change in y-values; Horizontal distance = change in x-values
So, $\text{Slope} = \frac{\text{change in } y\text{-values}}{\text{change in } x\text{-values}}$

Step2: Calculate change in y-values

Subtract y-coordinates: $5 - 2 = 3$

Step3: Calculate change in x-values

Subtract x-coordinates: $8 - 3 = 5$

Step4: Compute the slope

Substitute values into the slope formula: $\text{Slope} = \frac{3}{5}$

Answer:

First, fill the fraction as $\frac{\text{change in } y\text{-values}}{\text{change in } x\text{-values}}$. The slope of line $m$ is $\frac{3}{5}$.