Question

the amount of money m, in dollars, paul earns can be represented by the equation m = 12.5h + 11, where h is the number of hours paul works. which of the following is the best interpretation of the number 11 in the equation?
the total amount of money, in dollars, paul earns after working for h hours
the amount of money, in dollars, paul earns each hour
the amount of money, in dollars, paul earns in addition to an hourly wage
the total amount of money, in dollars, paul earns after working for one hour

Explanation:

Step1: Analyze the linear equation

The equation is \( M = 12.5h + 11 \), where \( M \) is total money and \( h \) is hours worked. In a linear equation \( y = mx + b \), \( b \) is the y - intercept (constant term), representing a fixed amount. Here, 12.5 is the hourly rate (slope, \( m \)), and 11 should be a fixed amount Paul earns regardless of hours (like a base pay or money earned in addition to hourly wage when \( h = 0 \)).

Step2: Evaluate each option

• Option 1: "The total amount of money, in dollars, Paul earns after working for h hours" - This is \( M \), not 11.
• Option 2: "The amount of money, in dollars, Paul earns each hour" - This is 12.5 (the slope), not 11.
• Option 3: "The amount of money, in dollars, Paul earns in addition to an hourly wage" - When \( h = 0 \) (no hours worked), \( M = 11 \). So this means even without working hours, he has 11 dollars, which is an amount in addition to hourly wage (since hourly wage depends on \( h \)). This fits.
• Option 4: "The total amount of money, in dollars, Paul earns after working for one hour" - For \( h = 1 \), \( M=12.5(1)+11 = 23.5\), not 11.

Answer:

The option "The amount of money, in dollars, Paul earns in addition to an hourly wage" (the third option among the given choices for the interpretation of 11).