Question

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

Explanation:

Step1: Choose two points on the line

Let's take two points on the line, for example, \((-3, 2)\) and \((1, -2)\) (we can also use other points, but these are clear from the graph).

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

The formula for \(\Delta y\) is \(y_2 - y_1\). Using the points \((-3, 2)\) as \((x_1, y_1)\) and \((1, -2)\) as \((x_2, y_2)\), we have \(\Delta y = -2 - 2 = -4\).

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

The formula for \(\Delta x\) is \(x_2 - x_1\). So, \(\Delta x = 1 - (-3) = 1 + 3 = 4\).

Step4: Calculate the slope

The slope \(m=\frac{\Delta y}{\Delta x}\). Substituting the values of \(\Delta y\) and \(\Delta x\), we get \(m = \frac{-4}{4}=-1\).

Alternatively, we can use the "rise over run" by looking at the graph. From one point to another, if we go down 4 units (rise is -4) and right 4 units (run is 4), then slope is \(\frac{-4}{4}=-1\).

Answer:

Rise (\(\Delta y\)) = \(-4\)
Run (\(\Delta x\)) = \(4\)
Slope = \(\frac{\Delta y}{\Delta x} = -1\)