Question

The graph below illustrates 2 intersecting lines. If a new line is drawn so that it passes through the red line at y = 0 and the blue line at x = –1, what is the slope of the new line?

Answer 1

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

$m = \dfrac{y_2 - y_1}{x_2 - x_1}$,

where $(x_1, y_1)$ and $(x_2, y_2)$ are points on the line that you are trying to find.

Let's "plug in" our values for the slope formula:

$m = \dfrac{-2 - 0}{-1 - (-4)} = \dfrac{-2}{3} = - \dfrac{2}{3}$

We can see that the slope of the line would be -2/3.