Learn Before
Interpreting the Slope and -Intercept of
Sam's weekly delivery van cost is modeled by the linear equation , where is the weekly cost in dollars and is the number of miles he drives. This practical equation matches the slope-intercept form , replacing standard variables with descriptive ones that match the context.
ⓐ Find when : Sam's cost is $60 per week when he drives miles.
ⓑ Find when : His cost is $185 when he drives miles.
ⓒ Interpret the slope and -intercept:
- The slope indicates that the weekly cost, , increases by $0.50 for each additional mile driven, .
- The -intercept is , meaning that when the number of miles driven is , the initial weekly cost is $60.
ⓓ Graph the equation: Graphing this real-world application requires a scaled rectangular coordinate system to accommodate larger quantities. Start at the -intercept . To make graphing the slope easier, write it as a fraction and multiply the numerator and denominator by to get the equivalent fraction . From the intercept, count a rise of and a run of to locate the next point at . Draw a straight line connecting these points to represent the cost function.
0
1
Tags
OpenStax
Intermediate Algebra @ OpenStax
Ch.3 Graphs and Functions - Intermediate Algebra @ OpenStax
Algebra
Related
Interpreting the Slope and -Intercept of
Interpreting the Slope and -Intercept of
Interpreting the Slope and -Intercept of
Interpreting the Slope and -Intercept of
An environmental scientist is modeling the rise in sea levels over time. To make the mathematical model more practical for a professional report, the scientist makes several adjustments to the standard linear equation and its graph. Match each action to the correct mathematical term used to describe it.
An analyst at a logistics company is creating a linear equation to model fuel consumption relative to the distance traveled by delivery trucks. Instead of using the generic slope-intercept form , the analyst uses the formula , where represents fuel and represents distance. According to the standard practices for modeling real-world data, what is the primary purpose of choosing these context-specific letters?
When grounding abstract linear equations into practical scenarios, the practice of extending the boundaries of a coordinate system to fit the full span of real-world data is known as using descriptive variables.
Grounding Linear Equations in Practical Scenarios
A technician measuring the voltage of a circuit over time finds that the readings reach volts, which far exceeds the standard to limits of a coordinate grid. To properly fit this data on a graph, the technician must extend the boundaries of the grid, a practice known as using ____ axes.
Learn After
A delivery contractor uses the equation to determine his weekly van expenses, where is the total cost in dollars and is the number of miles driven. In this business model, what does the value 60 represent?
A corporate logistics department uses the mathematical model to forecast the weekly operating expenses of their delivery vans. Match each part of the equation with its correct operational meaning to verify your understanding of the cost model.
In the delivery van cost model , the value 0.5 represents the cost in dollars added to the weekly total for each additional mile driven.
Identifying the Vertical Intercept of the Cost Model
A fleet manager is using the linear equation to visualize weekly delivery costs on a graph. Arrange the following steps in the correct order to graph this cost model using the rise and run method described in the text.