To find the equation of the linear function, we need to determine the slope, `m`, and the y-intercept, `b`.
Let's create two ordered pairs, `(x, y)`, using the given information. The first ordered pair will represent last year's order of 4 cubic yards of soil and $220 spent, `(4, 220)`. The second ordered pair will represent this year's order of 7 cubic yards of soil and $340 spent, `(7, 340)`.
We can use these ordered pairs to find the slope, `m`:
m = (change in y)/(change in x) = (y2 - y1)/(x2 - x1) = (340 - 220)/(7 - 4) = 120/3 = 40
Now that we have the slope, `m`, we can find the y-intercept, `b`, by substituting one of the ordered pairs into the slope-intercept form of a linear equation, `y = mx + b`, and solving for `b`.
Using the first ordered pair, we substitute `x = 4` and `y = 220`:
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
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)
1 answer