Question

identify the slope
find the slope.
slope $m = \frac{rise}{run} = \frac{y_2 - y_1}{x_2 - x_1}$
graph of a line on a coordinate plane
rise ($\delta y$) = $\square$
run ($\delta x$) = $\square$
slope = $\frac{\delta y}{\delta x} = \square$

Explanation:

Step1: Identify two points on the line

Looking at the graph, we can take two points: let's say \((0, -3)\) and \((2, 1)\) (we can also use other points, but these are clear).

Step2: Calculate the rise (\(\Delta y\))

Rise is the change in \(y\)-coordinates, so \(\Delta y = y_2 - y_1\). Using the points \((0, -3)\) and \((2, 1)\), \(y_2 = 1\), \(y_1 = -3\). So \(\Delta y = 1 - (-3) = 4\).

Step3: Calculate the run (\(\Delta x\))

Run is the change in \(x\)-coordinates, so \(\Delta x = x_2 - x_1\). Using the points \((0, -3)\) and \((2, 1)\), \(x_2 = 2\), \(x_1 = 0\). So \(\Delta x = 2 - 0 = 2\).

Step4: Calculate the slope

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

Answer:

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