For each situation, write a linear function using meaningful variables.

Question

For each situation, write a linear function using meaningful variables. Find and interpret the slope and y-intercept.

a). For each dollar a driver spends on gas, she can drive 15 miles. Assume she bought her car with 20,000 miles on it already. Write a linear function to model how many miles are on her car based on how much she spends on gas.

b). A man has a starting weight of 205 pounds and is losing 10 pounds each month. Model his weight with a linear function.

Answer 1

First of all, y = mx +b is called the "slope-intercept" form of a linear equation. The coefficient of x is the slope, so m = slope. b is the y-intercept, or where the line crosses the y-axis. This is the starting point of any given situation.

a. For the first situation, the driver gets 15 miles per dollar spent, and you need a model for total miles on the car.

M = total miles, and d = $1 spent on gas.

The total miles include the 20,000 already on the odometer, plus 15 multiplied by each dollar spent:

M(d) = 20,000 + 15d, or in slope-intercept form: M(d) = 15d + 20,000.

The slope is 15, which is the number of miles per dollar spent, and the y-intercept is 20,000, which is the initial mileage.

b. Let's use W for weight and m for months. The starting point, or b, is 205. The slope is -10 because that's how much the man is losing each month: W = -10m +205.

I hope this helps, and let me know if you have any more questions!

Happy mathing!

Liz Z.