What is the slope of the line passing through the points two, negative two and four, eight?
In order to calculate the slope or the gradient of a line, we need to subtract the 𝑦-coordinates, subtract the 𝑥-coordinates, and then divide our two answers. We use the formula 𝑦 two minus 𝑦 one divided by 𝑥 two minus 𝑥 one, where our 𝑥- and 𝑦-values are the ordered pairs two, negative two and four, eight.
Substituting these values into the formula gives us eight minus negative two divided by four minus two. Eight minus negative two is 10. Four minus two is two, which leaves us with 10 divided by two. As 10 divided by two is equal to five, our slope or gradient of the line that passes through the two points is equal to five.
As this is a positive number, our line will slope upwards from left to right. We can demonstrate this on a coordinate axis. If we plot the ordered pairs or coordinates two, negative two and four, eight and then draw a line that passes through both points, we can see that this is a positive slope because it is going upwards from left to right.
If we create a right-angle triangle, we can see that the difference between the 𝑦-coordinates eight and minus two is 10. To get from minus two to eight, we have to add 10. In the same way, moving along the 𝑥-axis from two to four involves adding two. 10 divided by two is equal to five. Therefore, the slope of the line passing through the two points is five.