draw a line representing the “rise” and a line representing the “run” of the line. state the slope of the…

Explanation:

Step1: Identify two points on the line

Looking at the graph, the line passes through ((-8, 0)) and ((0, -8))? Wait, no, let's check the coordinates. Wait, the x - axis and y - axis: let's take two clear points. Let's see, when (x = 0), (y=-8)? Wait, no, maybe ((-8,0)) and ((0, - 8)) is not correct. Wait, another way: let's find two points. Let's take the y - intercept and another point. Wait, the line goes through ((-8,0)) and ((0, - 8))? Wait, no, let's calculate the slope. Wait, maybe the two points are ((-8,0)) and ((0, - 8))? Wait, no, let's check the rise and run. Wait, actually, let's take two points: let's say ((-8,0)) and ((0, - 8)). The rise is the change in (y), so from (y = 0) to (y=-8), the change is (- 8-0=-8). The run is the change in (x), from (x=-8) to (x = 0), the change is (0-\left(-8\right)=8). Then the slope is (\frac{\text{rise}}{\text{run}}=\frac{-8}{8}=- 1). Wait, but maybe I made a mistake in points. Wait, another approach: let's take two points on the line. Let's see, the line passes through ((-8,0)) and ((0, - 8))? Wait, no, maybe ((-8,0)) and ((0, - 8)) is correct. Wait, let's check the graph again. The line has a negative slope. Let's take two points: when (x=-8), (y = 0); when (x = 0), (y=-8). So the rise (change in (y)) is (y_2 - y_1=-8 - 0=-8). The run (change in (x)) is (x_2 - x_1=0-\left(-8\right)=8). Then the slope is (\frac{\text{rise}}{\text{run}}=\frac{-8}{8}=-1).

Step2: Calculate the slope

The formula for slope (m=\frac{y_2 - y_1}{x_2 - x_1}). Let ((x_1,y_1)=(-8,0)) and ((x_2,y_2)=(0, - 8)). Then (m=\frac{-8 - 0}{0-\left(-8\right)}=\frac{-8}{8}=-1).

Answer:

The slope of the line is (-1)