Let \(x\) be the number of times Tony drives to visit his grandma, and let \(y\) 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 \(y\) represents the amount of change and \(x\) the number of visits, we can relate all the variables and quantities using a linear equation:
\(y=6-1.25x\)
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 \(y\) and \(x\)-intercepts.
- To find the \(y-intercept\) we just need to replace \(x\) with zero and solve for \(y\):
\(y=6-1.25x\)
\(y=6-1.25(0)\)
\(y=6\)
So, our first point is (0,6)
- To find the \(x-intercept\) we just need to replace \(y\) with zero and solve for \(x\):
\(0=6-1.25x\)
\(-6=-1.25x\)
\(x=\frac{-6}{-1.25}\)
\(x=4.8\)
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:
