write an equation for the linear function: The cost of renting a car is a flat$26, plus an additional 0.23 cents per mile that you drive. How far can you drive for $87?

y= total cost

x= number of miles

y=.23x + 26

Since they give you the total amount you can spend (y) plug that in and solve for x

87=.23x +26
87-26=.23x
61=.23x
265.22=x

87=.23x +26

87-26=.23x
61=.23x
265.22=x

To find the distance you can drive for $87, we can use the equation for the linear function. Let's assume the distance you can drive is represented by 'd' in miles.

According to the given information, the cost of renting a car is a flat $26, plus an additional 0.23 cents per mile. This can be written as:

Cost = 26 + 0.23d

We need to find the distance 'd' for a cost of $87. So, we can set up the equation:

87 = 26 + 0.23d

To isolate 'd', we can subtract 26 from both sides of the equation:

87 - 26 = 26 - 26 + 0.23d
61 = 0.23d

Now, we can solve for 'd' by dividing both sides of the equation by 0.23:

61 / 0.23 = 0.23d / 0.23
265.22 = d

Therefore, you can drive approximately 265.22 miles for $87.

To write an equation for the linear function that represents the relationship between the cost of driving and the distance driven, we can use the information given.

The cost of renting a car is a flat $26, which means regardless of the distance driven, you will have to pay $26. This can be represented as the y-intercept of the linear equation.

In addition to the flat cost, there is an additional charge of 0.23 cents per mile. Let's denote the distance driven as "x" (in miles). Hence, the additional charge for the distance driven can be represented as 0.23x.

To calculate how far you can drive for $87, we need to determine the value of "x" in the equation when the cost (y) is $87. So, we have:

y = 0.23x + 26,

where "y" is the cost and "x" is the distance driven in miles.

Setting y = 87:

87 = 0.23x + 26.

To solve for "x," we will isolate the variable:

87 - 26 = 0.23x.

61 = 0.23x.

Now, divide both sides by 0.23:

61 / 0.23 = x.

x ≈ 265.22.

Therefore, you can drive approximately 265.22 miles for $87.