Question

mat100 - 04 college algebra 2025 - 3
3.10 - applications of slope - intercept form
mastery 25%
current objective
graph and interpret applications of slope - intercept
first up, lets review the assignments learning objectives
get familiar with this topic by reviewing instruction and answering a couple of questions.
question
bruce drives his car for his job. the equation $r = 0.575m+42$ models the relation between the amount in dollars, $r$, that he is reimbursed and the number of miles, $m$, he drives in one day. interpret the slope of the equation.
select the correct answer below:
the slope, .575, means that the total amount bruce is reimbursed in one day increases by .575 dollars for each mile he drives on that day.
the slope, .575, means that the total amount bruce is reimbursed in one day increases by 1 dollar for each .575 miles he drives on that day.
the slope, 42, means that the total amount bruce is reimbursed in one day increases by 42 dollars for each mile he drives on that day.
the slope, 42, means that the total amount bruce is reimbursed in one day increases by 1 dollar for each 42 miles he drives on that day.

Explanation:

Step1: Recall slope - intercept form

The slope - intercept form of a linear equation is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept. In the given equation $R = 0.575m+42$, $m$ (the variable representing miles) is the independent variable and $R$ (the amount reimbursed) is the dependent variable. The slope of the line is $0.575$.

Step2: Interpret the slope

The slope represents the rate of change of the dependent variable with respect to the independent variable. Here, for every unit increase in the number of miles $m$ (i.e., for each additional mile driven), the amount $R$ that Bruce is reimbursed changes. Since the slope is $0.575$, for each mile he drives, the amount he is reimbursed increases by $0.575$ dollars.

Answer:

The slope, $.575$, means that the total amount Bruce is reimbursed in one day increases by $.575$ dollars for each mile he drives on that day.