Find the slope of the line between the two points shown.
We can find the slope of a line between two points as long as we know the coordinates of both points. Since these two points lie on a function whose equation we know, we can use the function to determine the coordinates of the points.
When x = 2 we have f(2) = (2)2 = 4, so the coordinates of the first point are (2, 4).
When x = 4 we have f(4) = (4)2 = 16 so the coordinates of the second point are (4, 16).
Now that we know the coordinates of both points we can calculate the rise and run:
rise = 16 - 4 = 12
run = 4 - 2 = 2.
The slope of the line between these two points is
To think of this in a more formula-oriented way, we have a = 2 and b = 4, so
f(a) = 4 and f(b) = 16.
Then the slope of the line between the two points is