A DJ charges $250 for 1 hour of work and charges $410 for 3 hours of work. Write an equation that models this situation. Let "x" represent the number of hours worked and "y" represent the cost to hire the DJ.
Thank you for the help! I appreciate it.
I meant to say help instead of fall. Oops!
*instead of galp.
I hate autocorrect.
He charges an extra $160 for 2 hours, or $80/hr after the first hour. So, for x hours (x>2),
y = 250 + 80x
Thank you so much, Steve!
To write an equation that models this situation, we can use a linear equation in the form of y = mx + b, where "y" represents the cost to hire the DJ and "x" represents the number of hours worked.
From the given information, we know that when the DJ works for 1 hour, the cost is $250, and when the DJ works for 3 hours, the cost is $410.
Let's calculate the slope, "m," of the equation:
m = (change in y) / (change in x)
m = (410 - 250) / (3 - 1)
m = 160 / 2
m = 80
The slope of the equation is 80.
Now, we need to find the y-intercept, "b," which represents the cost when the DJ works 0 hours. We can use one of the given data points to determine this:
Using the data point (1, 250):
250 = 80(1) + b
250 = 80 + b
Subtracting 80 from both sides, we get:
b = 250 - 80
b = 170
Therefore, the y-intercept, b, is 170.
Now we can write the equation:
y = 80x + 170
This equation models the situation where "x" represents the number of hours worked and "y" represents the cost to hire the DJ.