The cost of driving a car includes both fixed ans mileage costs. Assume that it costs $152.20 per month for insurance and car payments ans $0.22 per mile for gasoline oil and routine maintenance.

(a) Find value m and b so that y-mx=b modeks the monthly cost of driving the car x miles.
(b) What does the value of b represent.

.22 is a rate so that is our slope m

152.20 is your constant or fixed cost so that is b.

Can you write the equation now?

Thank you so much. I hope I can do it from here.

To find the values of m and b that model the monthly cost of driving the car, we need to understand the equation y = mx + b. Here, y represents the monthly cost of driving the car, x represents the number of miles driven, and m and b are the values we need to determine.

(a) To begin, we know that the fixed cost, which includes insurance and car payments, is $152.20 per month. This cost remains the same regardless of the number of miles driven. So, we can say that the fixed cost is the y-intercept, b. Therefore, b = $152.20.

Next, we know that the mileage cost, which includes gasoline, oil, and routine maintenance, is $0.22 per mile. This cost increases linearly with the number of miles driven. So, we can say that the mileage cost is represented by the slope, m.

Now, we need to determine the value of m. Since the mileage cost is $0.22 per mile, we can think of this as the cost per unit of x (cost per mile). In other words, the slope is the change in cost (y) per unit change in miles driven (x).

Therefore, m = $0.22.

So, the equation that models the monthly cost of driving the car x miles is:
y = 0.22x + 152.20

(b) The value of b in this equation represents the fixed costs, which includes insurance and car payments. It is the constant term in the equation, which does not change with the number of miles driven. In this case, b = $152.20 represents the monthly cost of these fixed expenses.

In summary, the value of b represents the amount you have to pay each month for insurance and car payments, regardless of the number of miles driven.