Question

identify the slope
find the slope.
slope $m = \frac{\text{rise}}{\text{run}} = \frac{y_2 - y_1}{x_2 - x_1}$
(4, 3)
(-2, -1)
rise ($\delta y$) = $\square$
run ($\delta x$) = $\square$
slope = $\frac{\delta y}{\delta x} = \square$

Explanation:

Step1: Calculate Rise (Δy)

Rise is the difference in y - coordinates. Using points \((-2, -1)\) and \((4, 3)\), \(\Delta y=y_2 - y_1=3-(-1)=4\)

Step2: Calculate Run (Δx)

Run is the difference in x - coordinates. Using points \((-2, -1)\) and \((4, 3)\), \(\Delta x=x_2 - x_1=4-(-2)=6\)

Step3: Calculate Slope

Slope is \(\frac{\Delta y}{\Delta x}\), so \(\frac{4}{6}=\frac{2}{3}\) (simplified)

Answer:

Rise (\(\Delta y\)) = \(4\)
Run (\(\Delta x\)) = \(6\)
Slope = \(\frac{2}{3}\)