A local specialty delivery service charges a fee of 5 for...

A local specialty delivery service charges a fee of $\$ 5$ for each delivery plus 55 cents for each mile over 10 miles. a. Write an equation for the cost in dollars for a delivery of $m$ miles over 10 miles. (Note: A 15 -mile delivery would be represented by $m=5 .$ b. Create a table of points that satisfy the equation found in part a. c. Create a graph for the equation using your points. Remember to label the graph with units.

A local specialty delivery service charges a fee of $\$ 5$ for each delivery plus 55 cents for each mile over 10 miles.
a. Write an equation for the cost in dollars for a delivery of $m$ miles over 10 miles. (Note: A 15 -mile delivery would be represented by $m=5 .$
b. Create a table of points that satisfy the equation found in part a.
c. Create a graph for the equation using your points. Remember to label the graph with units.

Key Concepts

Graphing Linear Functions

Graphing linear functions involves plotting the calculated points from the table on a coordinate grid and drawing a straight line through them. It is important to label the axes with the proper units and to ensure that the scale accurately reflects the relationship. This visual representation helps in understanding the continuous, linear relationship between the variables.

Table of Values

A table of values is a systematic way to organize input values along with their corresponding outputs according to the function. This tool is used to verify the behavior of the function, check for consistency, and provide data points that can be used to construct or analyze the graph of the relationship.

Linear Equations

A linear equation represents a constant rate of change between two variables and is typically written in the slope-intercept form, y = mx + b. This form simplifies the identification of the slope (m), representing the rate of change, and the y-intercept (b), representing the starting value or fixed cost in a model.

Fixed and Variable Costs

Cost models often combine a fixed fee with a variable fee that depends on an additional parameter (for example, distance or quantity). The fixed cost is incurred regardless of the consumption level, while the variable cost changes proportionally with the level of usage. Together, they form the complete cost function.

Rate of Change (Slope)

The rate of change in a linear model indicates how much the dependent variable (in this case, cost) changes for each unit increase in the independent variable (such as extra miles). This is a critical element in creating accurate models, showing the additional cost incurred per unit increase.

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