Let [tex] x [/tex] be the number of times Tony drives to visit his grandma, and let [tex] y [/tex] represent the amount of change Tony has in his car.
Since he pays $1.25 in tolls every time he visit his grandma, the amount of change in his car is going to decrease by $1.25 every visit. We know form our problem that he initially has 6 dollars in change in his car. Since [tex] y [/tex] represents the amount of change and [tex] x [/tex] the number of visits, we can relate all the variables and quantities using a linear equation:
[tex] y=6-1.25x [/tex]
To graph our linear equation, we just need to find two points and join them with a line.
The easiest points we can find are the [tex] y [/tex] and [tex] x [/tex]-intercepts.
- To find the [tex] y-intercept [/tex] we just need to replace [tex] x [/tex] with zero and solve for [tex] y [/tex]:
[tex] y=6-1.25x [/tex]
[tex] y=6-1.25(0) [/tex]
[tex] y=6 [/tex]
So, our first point is (0,6)
- To find the [tex] x-intercept [/tex] we just need to replace [tex] y [/tex] with zero and solve for [tex] x [/tex]:
[tex] 0=6-1.25x [/tex]
[tex] -6=-1.25x [/tex]
[tex] x=\frac{-6}{-1.25} [/tex]
[tex] x=4.8 [/tex]
Our second point is (4.8,0)
Now we can join those two points with a line.
we can conclude that the graph that represents the change Tony has in his car is the one in the picture:
