The student council is buying school T-shirts to sell during a fundraiser. The cost (y) of school T-shirts is a linear function of the number of T-shirts bought (x). The student council can buy 100 T-shirts for $825 and 300 T-shirts for $2,425.
Write an equation in slope-intercept form that represents this situation.
Graphy the equation on the coordinate plane for 0 to 100 100T-shirts. Explain how you found the answer
consider the given data as two ordered pairs
(100,825) and (300,2425)
treat it like you would if you worked with y = mx + b
slope = (2425 - 825)/(300-100) = 8
so y = 8t + b
for (100,825)
825 = 8(100) + b
b = 25
y = 8t + 25
8t+24
To write an equation in slope-intercept form, we need to find the slope and the y-intercept.
Let's use the given information to find the slope, m:
The student council can buy 100 T-shirts for $825, so the cost per T-shirt can be calculated as follows:
Cost per T-shirt = Total cost / Number of T-shirts
Cost per T-shirt = $825 / 100 = $8.25
The student council can also buy 300 T-shirts for $2,425, so we can calculate the cost per T-shirt in the same way:
Cost per T-shirt = $2425 / 300 = $8.08
Now, we can find the slope, m, using the formula:
m = (change in y) / (change in x)
(change in y) = cost per T-shirt = $8.25 - $8.08 = $0.17
(change in x) = 100 - 300 = -200
m = $0.17 / -200 = -0.00085
Now, let's find the y-intercept, b:
We know that when 100 T-shirts are bought, the cost is $825. This gives us the point (100, 825).
Using the slope-intercept form, y = mx + b, we can substitute the values we have to solve for b:
825 = -0.00085 * 100 + b
825 = -0.085 + b
b = 825 + 0.085
b ≈ 825.085
Now we have the equation in slope-intercept form:
y = -0.00085x + 825.085
To graph the equation on the coordinate plane from 0 to 100 for 100 T-shirts, we can plot the points for each value of x from 0 to 100 and connect them with a line.
Here are the data points:
(0, 825.085)
(10, 825.085 - 0.00085 * 10)
(20, 825.085 - 0.00085 * 20)
...
(100, 825.085 - 0.00085 * 100)
Plot these points on a coordinate plane and connect them with a line. The line represents the equation y = -0.00085x + 825.085.