Question

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 values are given in the table below.

Option 1: Find the equation representing this linear relationship.
Option 2: Calculate the daily operating cost when 60 students visit.
Option 3: Determine the number of students when the daily operating cost is $1200.
Option 4: Analyze the cost per student for 40 visitors.

Answer 1

To solve this problem, you need to find the equation representing the linear relationship between the number of student visitors and the daily operating cost, calculate the daily operating cost when a specific number of students visit, determine the number of students when the daily operating cost is given, and analyze the cost per student for a specific number of visitors.

Step-by-step explanation:

Option 1: To find the equation representing the linear relationship between the number of student visitors and the daily operating cost, we can use the equation for a straight line, which is y = mx + b. In this equation, y represents the daily operating cost and x represents the number of student visitors. To find the values of m and b, we can use the given sample values from the table.

Option 2: To calculate the daily operating cost when 60 students visit, we can substitute x = 60 into the equation from Option 1 and solve for y.

Option 3: To determine the number of students when the daily operating cost is $1200, we can substitute y = 1200 into the equation from Option 1 and solve for x.

Option 4: To analyze the cost per student for 40 visitors, we can substitute x = 40 into the equation from Option 1 and solve for y. The cost per student can be found by dividing the total cost by the number of students.