The budget for the Grant Center assumes a linear relationship between the number of student visitors and the daily operating cost of the center. Some sample (number of students, operating cost) values are given in the table below.
Number of Students
Daily Operating Cost
$1,050 a. Use the given data to write an equation showing how operating cost, C, depends on the number of students, x. Explain or show how you found the equation.
For parts (b)–(d), write equations or inequalities for each question. Then do the required calculations or solve the equation to find each answer.
b. For what number of student visitors will the daily operating cost be $690?
c. What will be the operating cost on a day with 12 student visitors?
d. How many students can visit the center if the operating cost is to be at most $1,000?
The students at the center found many linear functions. Find an equation for each line.
a. The line passes through the points (0, 8) and (4, 13).
b. The line has slope –3 and passes through the point (1, 4).
c. The line passes through points (1, 1) and (3, 9)
At Metropolis Middle School, the student government earns money by recycling cans and bottles after school events.
The graph shows some sample (attendance, containers) data, along with a line modeling the pattern in the data.
a. Use the linear model to estimate answers for the next questions. Explain how each estimate can be found from the graph.
i. About how many containers will be recycled if 125 people attend a concert?
ii. What attendance at a basketball game will produce about 125 containers to be recycled?
b. Use the points (200, 100) and (50, 25) to find an equation in the form for the modeling line. Show your work.
C. Explain what the slope and the y-intercept in your equation tell about the relationship between the number of containers to be recycled and the attendance at a school event.