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.(1 point)

Answer 1

To find the equation of the linear function in the form \( y = mx + b \), we first need to determine the slope \( m \) and the y-intercept \( b \).

We have two points based on Alayah's orders:

1. For last year: \( (4, 220) \)
2. For this year: \( (7, 340) \)

First, we can calculate the slope \( m \) using the formula:

\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Here, \( (x_1, y_1) = (4, 220) \) and \( (x_2, y_2) = (7, 340) \).

Now substituting the values in:

\[
m = \frac{340 - 220}{7 - 4} = \frac{120}{3} = 40
\]

Next, we can use one of the points and the slope to find the y-intercept \( b \). We'll use the point \( (4, 220) \):

Using the equation \( y = mx + b \):
\[
220 = 40(4) + b
\]
\[
220 = 160 + b
\]
\[
b = 220 - 160 = 60
\]

Now, we have \( m = 40 \) and \( b = 60 \). 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:

\[
y = 40x + 60
\]