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)
To write the equation of the linear function that models the relationship between the number of cubic yards of soil ordered and the total cost, we need to find the slope (m) and the y-intercept (b).
We are given two points on the line: (4, 220) and (7, 340). Let's use these points to find the slope.
The slope (m) can be calculated using the formula:
m = (y2 - y1) / (x2 - x1)
Using our two points, let's substitute the values:
m = (340 - 220) / (7 - 4)
m = 120 / 3
m = 40
Now that we have the slope (m), let's find the y-intercept (b). We can use either point to do this.
Using the point (4, 220), we can substitute the values into the slope-intercept form equation (y = mx + b) and solve for b:
220 = 40 * 4 + b
220 = 160 + b
b = 220 - 160
b = 60
Now we have the slope (m = 40) and the y-intercept (b = 60). Let's write the equation of the linear function:
y = 40x + 60
So, the equation of the linear function that models the relationship between the number of cubic yards of soil ordered (x) and the total cost (y) is y = 40x + 60.
Using the given points (4, 220) and (7, 340), we can calculate the slope:
slope = (change in y) / (change in x)
slope = (340-220) / (7-4)
slope = 120 / 3
slope = 40
Now we can use the point-slope form to find the equation:
y - y1 = m(x - x1)
y - 220 = 40(x - 4)
y - 220 = 40x - 160
y = 40x + 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, where y represents the total cost and x represents the number of cubic yards of soil ordered.
Well, let's calculate the slope first. We know that the number of cubic yards of soil ordered increased from 4 to 7, and the cost increased from $220 to $340. So, the change in x is 7 - 4 = 3, and the change in y is $340 - $220 = $120.
Now, we can find the slope (m) by dividing the change in y by the change in x: m = 120/3 = 40.
Next, let's find the y-intercept (b). We can use either point, but let's use the first point (4, $220). Plugging these values into the slope-intercept form (y = mx + b), we can solve for b:
$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 (x) and the total cost (y) is:
y = 40x + 60.
To write the equation of the linear function, we need to find the slope (m) and the y-intercept (b).
First, let's find the slope (m). We can use the formula for slope, which is (change in y) / (change in x).
The change in y is the difference in cost, which is $340 - $220 = $120.
The change in x is the difference in the number of cubic yards, which is 7 - 4 = 3.
So, the slope (m) is (change in y) / (change in x) = $120 / 3 = $40.
Now, let's find the y-intercept (b). We can choose any point on the line to find the y-intercept. Let's use the point (4, $220) since that was our first data point.
We substitute this point into the slope-intercept form of a linear equation, y = mx + b, and solve for b.
$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.