To use the slope formula, we need to find two points. In this case, the points will be the point on the red line where y = 0 and the point on the blue line where x = -1. So, let's find those points completely so that we can properly use the slope formula.
Let's find the x-value of the coordinate on the red line where y = 0. To do this, let's find where the red line crosses y = 0 and find the x-value associated with it. You can see that the red line reaches y = 0 (the x-axis) at x = -4. So, one of our points is (-4, 0).
The next point is where the blue line crosses x = -1. To find the y-value associated with the coordinate of x = -1, let's find where the blue line is at x = -1 and see the y-value of the blue line at that point. By the graph, you can see that whenever the blue line is at x = -1, its value is -2. Thus, another coordinate point is (-1, -2).
Now that we have two points, we can use our slope formula. The slope formula is
[tex]m = \dfrac{y_2 - y_1}{x_2 - x_1}[/tex],
where [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] are points on the line that you are trying to find.
Let's "plug in" our values for the slope formula:
[tex]m = \dfrac{-2 - 0}{-1 - (-4)} = \dfrac{-2}{3} = - \dfrac{2}{3}[/tex]
We can see that the slope of the line would be -2/3.
