Question

Kylie is comparing the cost of two housekeeping companies, DoItRight and CleanIt. The table describes the costs for DoItRight.

Hours, x 1.5 3 3.5 4.5

Total Cost, f(x) $26 $44 $50 $62


The cost of CleanIt Housekeeping is represented by g(x) = 10x + 16, where x represents the number of hours and g(x) represents the total cost in dollars.


Determine which company has the greater initial cost. Plot a point on the graph to represent the initial cost of that company.

Answer 1

First, find the cost function of DoItRight Housekeeping:

• Slope(m) = cost per hour =
  `(y_(2)-y_(1))/(x_(2)-x_(1))=(44-26)/(3-1.5)=(18)/(1.5)=12`

The y-intercept(b), representing the initial cost, can be calculated by substituting in values to the function:

`f(x)=12x+b\\26=12(1.5)+b\\b=26-18=8`

Therefore, the function for two companies are:

• The function for DoItRight is
  `f(x)=12x+8`
• The function for CleanIt is
  `g(x)=10x+16`

When comparing the two functions, it's shown how CleanIt has a greater y-intercept than DoltRight, meaning that CleanIt has a greater initial cost than DotRight. The y-intercept is when the graph intercepts the y-axis, therefore, the coordinates there would be (0, y-value), which, in this case for CleanIt company, will be (0, 16). While CleanIt has a greater y-intercept(initial cost), DoItRight has a greater slope, meaning they cost more per hour.