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 \( y = mx + b \), where \( y \) represents the total cost and \( x \) represents the number of cubic yards of soil, we first need to determine the slope \( m \) and the y-intercept \( b \).

We have two points based on Alayah's orders:

1. (4, 220) - This corresponds to 4 cubic yards for $220.
2. (7, 340) - This corresponds to 7 cubic yards for $340.

### Step 1: Calculate the slope \( m \)

The formula for the slope \( m \) is:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Using the two points (4, 220) and (7, 340):
- \( x_1 = 4 \), \( y_1 = 220 \)
- \( x_2 = 7 \), \( y_2 = 340 \)

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

### Step 2: Use one of the points to calculate \( b \)

We can use the slope-intercept form \( y = mx + b \) with one of the points to solve for \( b \). Let's use the point (4, 220).

Substitute \( m = 40 \) and \( (x, y) = (4, 220) \):
\[
220 = 40(4) + b
\]
\[
220 = 160 + b
\]
\[
b = 220 - 160 = 60
\]

### Step 3: Write the equation

Now that we have both \( m \) and \( b \), we can write the equation of the linear function:
\[
y = 40x + 60
\]

Thus, the final answer is:
\[
y = 40x + 60
\]