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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.

Sagot :

jessmzhou4

Answer:

First, find the cost function of DoItRight Housekeeping:

  • Slope(m) = cost per hour = [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}=\frac{44-26}{3-1.5}=\frac{18}{1.5}=12[/tex]

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

[tex]f(x)=12x+b\\26=12(1.5)+b\\b=26-18=8[/tex]

Therefore, the function for two companies are:

  • The function for DoItRight is [tex]f(x)=12x+8[/tex]
  • The function for CleanIt is [tex]g(x)=10x+16[/tex]

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.

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