If you rent a car for one day and drive 225 miles, the cost is $80. If you drive 350 miles in one day, the cost is $105. Let cm) represent the cost, in dollars, of driving m miles: a) Find a linear function C(m) that fits the data. b) Use the function of part (a) to find how much it will cost to rent a car for one day and drive it 475 miles. Also, find the number of miles you can drive for $155.

a)

And we want to find a function:

We can find the slope with this formula:

And then we can use the point   to find the intercept and we got:

So then the linear function is given by:

b) For this case we have that m = 475 so we can replace into the function to find the cost like this:

And for the other case we have a cost of 155 and we want to find the number of miles associated so we can do this:

Step-by-step explanation:

For this case we can define the following notation:

m= represent the miles travelled

C= represent the cost

Part a

For this case we have the following two points given:

And we want to find a function:

We can find the slope with this formula:

And then we can use the point   to find the intercept and we got:

So then the linear function is given by:

Part b

For this case we have that m = 475 so we can replace into the function to find the cost like this:

And for the other case we have a cost of 155 and we want to find the number of miles associated so we can do this:

72 is the answer to this problem