To begin, you are given two point that this function would intercept: (0,3) where the 0 is the original year (2000) and 3 is the amount of million cars sold. The next point would be (6,2.5) Where the 6 is the 6 years later and the 2.5 is the 2.5 million cars sold. Since we have 2 points, we can work out the gradient by finding the rate of change in y and dividing by the rate of change in x:
[tex] \frac{y_{1}- y_{2} }{x_{1}- x_{2} } [/tex]
We then substitute in the points:
[tex] x_{1} =3[/tex]
[tex] y_{1} =0[/tex]
[tex] x_{2} =2.5[/tex]
[tex] y_{2} =6[/tex]
[tex] \frac{3-2.5}{0-6} [/tex]
[tex] =\frac{0.5}{-6} [/tex]
[tex]=-.083[/tex]
Because we started on the y-intercept of (0,3), we already have our intercept value of 3. If we did not start with the y-intercept given, we could substitute in a point to solve for it:
Using point (2.5,6):
[tex]2.5=-0.083*6+c[/tex]
[tex]2.5=-0.5+c[/tex]
[tex]2.5+0.5=c[/tex]
[tex]c=3[/tex]
Hope this helps :)
