Question

HELP PLEASE!! The cost to fill a car's tank with gas and get a car wash is a linear function of the capacity of the tank. The costs of a fill-up and a car wash for three different customers are shown in the table. Write an equation for the function in slope-intercept form. Then, find the cost of a fill-up and a car wash for a customer with a truck whose tank size is 25 gallons.

Answer 1

The equation would be y=2.10x+3.25!

Also know as A lol

If you plug in 9 as x and add 3.25 it is an easy way to check the answers for further questions!

Have a good day! :-)

If it is not correct or doesn't look quite right or needs to show proof please comment!

Answer 2

`f(x)=2.1x+3.25`

Cost for truck = $55.75.

Explanation:

To right the linear equation in slope-intercept form, we first need to find the slop, which is defined

`m=(y_(2)-y_(1))/(x_(2)-x_(1))`

Now, we choose to points from the table
`(9, 22.15)` and
`(16, 36.85)`. Using this points, we calculate the slope.

`m=(36.85-22.15)/(16-9)=(14.7)/(7)=2.1`

Now, using one point and the slope, we find the point-slope form, which is gonna give us the slope-intercept form:

`y-y_(1)=m(x-x_(1)))\\y-22.15=2.1(x-9)\\y=2.1x-18.9+22.15\\y=2.1x+3.25`

Therefore, the right choice is the first one, because it's the only one that has this linear equation.

In addition, to find the cost for a car with 25 gallons of gas size, we just have to replace this number in the x-variable:

`y=2.1(25)+3.25=55.75`

Therefore, the cost for a truck with a tank size of 25 gallons, is $55.75.