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. Enter your answer in y=mx+b form.(
To find the equation of the linear function, we need to find the slope (m) and the y-intercept (b).
First, let's find the slope:
The change in the number of cubic yards of soil ordered is 7 - 4 = 3.
The change in the total cost is $340 - $220 = $120.
So the slope (m) is the change in the total cost divided by the change in cubic yards: m = 120 / 3 = 40.
Next, let's find the y-intercept:
We can choose either of the given data points to substitute into the equation. Let's use the cost of $220 when 4 cubic yards were ordered.
y = mx + b
220 = 40(4) + b
220 = 160 + b
b = 220 - 160
b = 60.
Therefore, the equation of the linear function that models the relationship between the number of cubic yards of soil ordered (x) and the total cost (y) is y = 40x + 60.