Janelle is planning to rent a car while on vacation. The...

Janelle is planning to rent a car while on vacation. The equation $$ C=0.32 m+15 $$ models the relation between the cost in dollars, $C$, per day and the number of miles, $m,$ she drives in one day. (a) Find the cost if Janelle drives the car 0 miles one day. (b) Find the cost on a day when Janelle drives the car 400 miles. (c) Interpret the slope and C-intercept of the equation. (d) Graph the equation.

Janelle is planning to rent a car while on vacation. The equation $$ C=0.32 m+15 $$ models the relation between the cost in dollars, $C$, per day and the number of miles, $m,$ she drives in one day.
(a) Find the cost if Janelle drives the car 0 miles one day.
(b) Find the cost on a day when Janelle drives the car 400 miles.
(c) Interpret the slope and C-intercept of the equation.
(d) Graph the equation.

Key Concepts

Graphing Linear Equations

Graphing a linear equation involves plotting the y-intercept on the coordinate plane and using the slope to determine additional points along the line. This visual representation aids in understanding the relationship between variables and can be used to forecast values, analyze trends, and identify key features of the modeled situation.

Y-Intercept

The y-intercept is the point where a linear function crosses the y-axis, representing the fixed or starting value of the function when the independent variable is zero. It often serves as the base fee, initial quantity, or fixed cost in real-world modeling and helps anchor the linear relationship in practical applications.

Function Evaluation

Function evaluation is the process of substituting a specific value for the independent variable in an equation to determine the corresponding value of the dependent variable. This fundamental concept is widely applicable in analyzing mathematical models, making predictions, and interpreting real-world scenarios.

Linear Functions

A linear function is an algebraic expression that models a relationship with a constant rate of change, typically written in the form y = mx + b. These functions describe situations where there is a proportional increase or decrease and a fixed starting value. They are fundamental in understanding how one variable depends linearly on another.

Slope

The slope of a linear function represents its rate of change; it quantifies how much the dependent variable changes for each unit increase in the independent variable. In practical terms, the slope is interpreted as the cost or benefit per unit of the variable being measured, providing crucial information about the sensitivity of the outcome to changes in the input.

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