Christopher D. answered • 12/28/18
Mathematician and Educator
All lines (in slope-intercept form) look like y = mx + b
So we need to figure out m (the slope), and b (the y-intercept).
Luckily, we have 2 points.
We know in 1998, there were 4760 electric cars; which means that when x=0 (meaning 0 years since 1998), y=4760
So we have the point (0, 4760)
We also know in 2001, there were 6680 electric cars; which means that when x=3 (again, meaning 3 years since 1998), y=6680
So we have the point (3, 6680)
We can find the slope by dividing the change in y ("rise") over the change in x ("run").
The change in y is 6680 - 4760 = 1920
The change in x is 3 - 0 = 3
Meaning that over 3 years, the number of electric cars increased by 1,920
This means that the average rate of change per year is 1920 / 3 = 640
Each year, there are 640 more electric cars (at least between 1998 and 2001).
This is our slope, m=640
Now we need b, the y-intercept. Luckily, we already have the y-intercept! Remember that we have the point (0, 4760), and the y-intercept is simply the point where x=0: the starting point. This point has x=0. This is out y-intercept: (0, 4760).
So b=4760
We can now write out equation: y = 640x + 4760
That is, the number of cars in a given year can be approximated as 4760 (the number of cars in 1998), plus 640 (the number of new cars per year) times the number of years that have passed since 1998 (our starting point). But the equation, y = 640x + 4760 is much easier to read. :)
