Learn Before
Comparison of and
Graphing the equations and on the same rectangular coordinate system clearly demonstrates the differences between linear equations with two variables versus a single variable. For the two-variable equation , the value of depends entirely on the chosen value of . Generating a table of values by selecting arbitrary -coordinates yields scattered ordered pairs such as (0, 0), , and . Plotting these points produces a slanted line that passes through the origin. Conversely, the single-variable equation lacks an variable, meaning the -value remains a constant regardless of any chosen -coordinate. Creating a table of values for this equation results in ordered pairs like , , and . Plotting these points produces a straight horizontal line that intersects the -axis at .
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Intermediate Algebra @ OpenStax
Ch.3 Graphs and Functions - Intermediate Algebra @ OpenStax
Algebra
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Graphing by Plotting Points
Graphing by Plotting Points
Comparison of and
Comparison of and
A corporate training department has a fixed annual budget of 5000 dollars for online course licenses, regardless of how many employees enroll. When this budget is graphed on a coordinate plane with the number of enrollments on the -axis and the total cost on the -axis, it forms a horizontal line. Which equation represents this horizontal line?
An office manager is graphing a fixed monthly subscription cost for a software service that remains constant regardless of the number of employees using it. This graph forms a horizontal line on a coordinate plane. The general equation for any horizontal line takes the form , which contains only the variable ____.
A project manager is tracking a fixed monthly subscription cost that does not change regardless of the number of users. On a coordinate plane, this fixed cost is represented by a horizontal line. Match each characteristic of a horizontal line with its correct mathematical description or property.
Identifying Fixed Costs as Horizontal Lines
A retail store manager is plotting a fixed monthly security fee on a coordinate plane. Because the fee is a constant amount regardless of the monthly sales volume , the graph is a horizontal line. True or False: The equation for this horizontal line is , it contains only the variable (no ), and it passes through the -axis at the point (0, b).
An accounting clerk is preparing a coordinate graph to show the company's fixed monthly internet cost of 120 dollars, which is represented by the horizontal line equation . To correctly display this constant cost on a financial report, the clerk decides to use the point-plotting method. Arrange the steps the clerk must follow to graph this horizontal line, from start to finish.
Graphing Fixed Software Costs: Properties of a Horizontal Line
Learn After
Match each linear equation with the correct description of its graph on a rectangular coordinate system.
A technician is monitoring two different automated systems on a coordinate screen. System A follows the equation and System B follows the equation . Which of the following accurately describes the visual difference between these two systems as they appear on the screen?
A technician is monitoring two different performance models on a coordinate screen. Model A follows the equation and Model B follows the equation . True or False: On the screen, Model B will appear as a horizontal line, while Model A will appear as a slanted line that passes through the origin.
Comparing Variable and Constant Performance Models
A technician is monitoring two different automated systems on a coordinate screen. System A follows the equation , which creates a slanted line passing through the origin. System B follows the equation , which creates a ________ line that reflects a constant output regardless of the -value.
Recalling Graph Characteristics of Linear Models
An inventory manager is graphing two shrinkage models for a quarterly report: a variable model () and a constant model (). Arrange the steps the manager must recall and follow to accurately graph and compare both equations.