Finding More Slopes

Let's try finding the slope of the line between these two flies:

The first fly is at point (2, 1), and the second fly is at point (4, 2). We can substitute this into our slope equation to find the slope of the line.

m = (y₂ - y₁) / (x₂ - x₁)
= (2 - 1) / (4 - 2)
= 1/2.

The line's slope is 1/2. If Joan finds a point on the line and then gives her tongue the same slope, she should be able to catch both flies:

Now let's find the slope of this line. Notice that the line slants down instead of up. Because the line is slanting down, its slope should be negative.

Before we can find the line's slope, we need to locate two points on the line. We can see that the line intersects the y-axis at the point (0, 4). Finding a second point is more difficult. We can try to be exact by finding a point on the line where two gridlines cross. One point like this is (2, 1). In this picture, the points we have chosen are colored blue:

Now we can use our slope equation to find the line's slope.

m = (y₂ - y₁) / (x₂ - x₁)
= (1 - 4) / (2 - 0)
= -3/2, or -1.5.

Our line's slope is a negative number, just as we predicted.