To find the equation of the linear function that models the relationship between the number of cubic yards of soil ordered (let's denote it as \( x \)) and the total cost (denote it as \( y \)), we can use the two data points provided.
The two data points we have are:
- When \( x = 4 \), \( y = 220 \)
- When \( x = 7 \), \( y = 340 \)
We can use these points to find the slope \( m \) of the line using the formula:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Substituting in our points \((x_1, y_1) = (4, 220)\) and \((x_2, y_2) = (7, 340)\):
\[ m = \frac{340 - 220}{7 - 4} = \frac{120}{3} = 40 \]
Now that we have the slope \( m = 40 \), we can use the point-slope form of the linear equation to find the y-intercept \( b \). We'll use one of the points, let's use \( (4, 220) \):
The point-slope form of the equation is given by:
\[ y - y_1 = m(x - x_1) \]
Substituting \( m = 40 \), \( x_1 = 4 \), and \( y_1 = 220 \):
\[ y - 220 = 40(x - 4) \]
Now simplify this equation:
\[ y - 220 = 40x - 160 \]
Add 220 to both sides:
\[ y = 40x + 60 \]
So, the equation that models the relationship between the number of cubic yards of soil ordered and the total cost is:
\[ y = 40x + 60 \]
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