The comparison of the initial values and rates of change of the functions indicates;
The function for Company A has an initial value of 500 while Company B has an initial value of 350. Company A has a greater initial value
The function for Company A has a rate of change of 12.5, while Company B has a rate of change of 15. So Company B has a greater rate of change
The steps used to evaluate the two job offers are presented as follows;
The equation for the total earnings for Company A can be found as follows;
Amount Company A will pay Gennaro for each item he sells = $12.50
Base salary Company A will pay Gennaro at the end of each month = $500
The equation for the total earnings, y is therefore;
y = 12.5·x + 500
The table of values for the amount Company B will pay Gennaro indicates that the amount paid for each item he sells is, which is the rate of change of the relationship is; (575 - 425)/(15 - 5) = 15
Therefore, Company B pays Gennaro $15 for each item he sells
The equation for total earnings for Company B is therefore;
y - 425 = 15 × (x - 5)
y = 15·x - 75 + 425
y = 15·x + 350
The above equation indicates that the initial value Company B pays Gennaro is $350
The initial value for Company A, 500 is larger than the initial value for Company B
The rate of change for Company B, 15 is larger than the rate of change for Company A