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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OpenStax
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.
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