Bruce drives his car for his job. The equation R=0.575 m+42...

Bruce drives his car for his job. The equation $R=0.575 m+42$ models the relation between the amount in dollars, $R$, that he is reimbursed and the number of miles, $m$, he drives in one day. (a) Find the amount Bruce is reimbursed on a day when he drives 0 miles. (b) Find the amount Bruce is reimbursed on a day when he drives 220 miles. (c) Interpret the slope and $R$ -intercept of the equation. (d) Graph the equation.

Bruce drives his car for his job. The equation $R=0.575 m+42$ models the relation between the amount in dollars, $R$, that he is reimbursed and the number of miles, $m$, he drives in one day.
(a) Find the amount Bruce is reimbursed on a day when he drives 0 miles.
(b) Find the amount Bruce is reimbursed on a day when he drives 220 miles.
(c) Interpret the slope and $R$ -intercept of the equation.
(d) Graph the equation.

Key Concepts

Linear Functions

A linear function models a relationship between two variables where the change is consistent across the domain. It is defined by a constant rate of change (the slope) and a fixed starting value (the intercept), making it useful for representing real-world relationships such as cost, distance, or time where one variable changes at a steady rate with respect to another.

Y-Intercept

The y-intercept of a linear equation is the value of the dependent variable when the independent variable is zero. It represents the starting value or initial condition in the context of a real-world problem, indicating the amount present without any contribution from the changing factor.

Slope

The slope in a linear equation indicates the rate at which the dependent variable changes with respect to the independent variable. It quantifies the effect of a one unit increase in the independent variable on the dependent variable, providing insight into proportional changes within the modeled scenario.

Graphing Linear Equations

Graphing linear equations involves plotting the line represented by the equation on a coordinate plane using the slope and y-intercept. This visual representation is key for understanding the relationship between variables as it shows both the constant rate of change and the starting point, making it easier to predict values and interpret the behavior of the function.

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