Last year, Alayah ordered 4 yd.³ of soil and spent $220. This year, she ordered 7 yd.³ 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 write the equation of the linear function, we need to find the values of m and b in the equation y = mx + b.
Let's use the points (4, 220) and (7, 340) to determine the values of m and b.
First, let's find the value of m, which represents the slope of the line. The slope is given by the formula:
m = (y₂ - y₁) / (x₂ - x₁)
Using the points (4, 220) and (7, 340), we have:
m = (340 - 220) / (7 - 4)
m = 120 / 3
m = 40
Now let's find the value of b, which represents the y-intercept of the line. We can substitute the value of m into the equation:
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 and the total cost is:
y = 40x + 60