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

Answer 1

Let's denote the number of cubic yards of soil as x and the total cost as y. We need to find the linear function that relates these two variables.

According to the given information,

When x = 4, y = 220.

So we have the ordered pair (4, 220).

Also, when x = 7, y = 340.

So we have the ordered pair (7, 340).

Now, let's find the slope of the line passing through these two points:

slope (m) = (y2 - y1) / (x2 - x1)
= (340 - 220) / (7 - 4)
= 120 / 3
= 40.

So we have m = 40.

Now, let's find the y-intercept (b). We can use the equation of a line in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.

Using the ordered pair (4, 220), we can substitute these values:

220 = 40 * 4 + b
220 = 160 + b
b = 220 - 160
b = 60.

So we have b = 60.

Therefore, 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) is:

y = 40x + 60.