Question

Computer repair companies use a fixed cost equation to determine how much to charge for an in-

house repair. For example, a technician charges $85 for a house call and $45 per hour. The fixed cost
equation is y = 85 +45x.
A. How are the slope and the y-intercept of the graph related to the equation?
B. What is the rate of change in the equation? How is the rate of change related to the slope of
the line represented by the equation? Explain.
line

Answer 1

A. In the equation
`\(y = 85 + 45x\),` the slope (45) represents the hourly rate of change, and the y-intercept (85) is the fixed cost for a house call.

B. The rate of change is $45 per hour, reflecting the slope, indicating the constant cost increase for each additional hour of repair.

A. In the fixed cost equation
`\(y = 85 + 45x\),` the slope is represented by the coefficient of
`\(x\),` which is 45, and the y-intercept is the constant term, which is 85. The slope
`(\(m\))` indicates the rate at which the cost increases per unit of the independent variable (in this case,
`\(x\)` , which represents the number of hours of repair). The y-intercept
`(\(b\))` is the fixed cost, the amount charged for the house call regardless of the number of hours.

B. The rate of change in the equation is given by the coefficient of
`\(x\),`which is 45. This means that for each additional hour of repair
`(\(x\))` , the cost increases by $45. The rate of change is synonymous with the slope of the line. In this context, it represents the incremental cost per hour of repair. The equation's slope indicates the constant rate at which the cost changes concerning the number of hours.

In summary, the slope (45) represents the rate of change or cost per hour of repair, and the y-intercept (85) represents the fixed cost, which is the cost incurred for the house call. Understanding these components is essential for interpreting and applying the fixed cost equation in the context of computer repair charges.