Question

Last year, Alayah ordered 4 cubic yards of soil and spent $220. This year, she orders 7 cubic yards of soil and spends $340. Write the equation of the linear function that models the relationship between the number of cubic yards of soil ordered and the total cost in y = mx + b form.

Answer 1

First, we need to find the slope, or rate of change, of the function. To do this, we can use the formula:

slope = (change in y) / (change in x)

In this case, the change in y is the difference in cost between the two orders ($340 - $220 = $120), and the change in x is the difference in the number of cubic yards ordered (7 - 4 = 3). So:

slope = 120 / 3 = 40

This means that for every additional cubic yard of soil ordered, the total cost increases by $40.

Next, we need to find the y-intercept, or the value of y when x is zero. In other words, how much would it cost if Alayah didn't order any soil? We can use either of the two data points to find this. Let's use the first one:

y = mx + b
220 = 4(40) + b
220 = 160 + b
b = 60

So the equation in y = mx + b form is:

y = 40x + 60

This means that the total cost (y) is equal to 40 times the number of cubic yards ordered (x), plus a base cost of $60.