The Key Club is hosting a banquet as a fundraiser. If 60 people attend, they make $500. If 80 people attend, they make $1500.
Write an equation in slope-intercept form to describe the situation.
To write an equation in slope-intercept form (y = mx + b), where y is the profit made and x is the number of people attending, we can use the given information:
1. When 60 people attend, they make $500.
2. When 80 people attend, they make $1500.
These points give us (x1, y1) = (60, 500) and (x2, y2) = (80, 1500).
Let's find the slope (m) of the line using these points:
m = (y2 - y1) / (x2 - x1)
m = (1500 - 500) / (80 - 60)
m = 1000 / 20
m = 50
So for every additional person that attends, the profits increase by $50.
Now that we have the slope, let's find the y-intercept (b). We can use either point for this, but we'll use the first point (60, 500):
y = mx + b
500 = 50(60) + b
500 = 3000 + b
b = 500 - 3000
b = -2500
Now we have the slope (m = 50) and the y-intercept (b = -2500). The slope-intercept form of the equation is:
y = 50x - 2500
This equation shows that the profit (y) is equal to 50 times the number of people attending (x) minus a fixed cost of $2500.