Answer:
y=29*x
Step-by-step explanation:
This problem is a linear function problem. We need at least two points to solve it. After finding two points we will compute the slope and then us the point-slope formula.
If you put 11 gallons of gasoline in your car it will allow you to drive 319 miles, this means that when x= 11 then, y=319. So the first point is (11,319). For the second point you now that if you have no gallons of gasoline then you won't be able to drive so, the second point is (0,0).
Now that we have to points we are able to compute the slope. The formula for the slope is:
[tex]m = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex].
this way
[tex]m = \frac{0-319}{0-11}[/tex].
[tex]m = 29[/tex].
Now that we have the slope, we can use the point-slope formula to get the equation. The point-slope formula is:
[tex](y-y_{1}) = m(x-x_{1})[/tex] (here it doesn't matter which point you use, you will get the same result).
Substituting the point (11,319) and the slope:
[tex](y-319) = 29(x-11)[/tex]
[tex]y-319 = 29x-319[/tex]
[tex]y = 29x[/tex]
And we finaly get the equation!
