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Comparison of and
Comparing the equations and highlights the difference between an equation with two variables and an equation with a single variable. In the two-variable equation , the value of depends directly on the chosen value of , meaning as the -coordinate changes, the -coordinate changes accordingly; visually, this produces a slanted line graph. Conversely, the one-variable equation specifies that is a constant value independent of ; because the -coordinate is always , graphing this equation yields a straight horizontal line.
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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 .
Learn After
A facility manager is using mathematical models to track operational costs. Match each equation to the description that correctly identifies its graphical representation and behavior.
A logistics analyst is reviewing two different freight cost models for a regional shipping route.
Model 1 is given by the equation , where represents the total cost and represents the weight of the shipment in tons.
Model 2 is given by the equation .
When these models are plotted on a coordinate plane, which statement correctly describes the graph of Model 2?
A logistics analyst is using two models to predict delivery phases. Model A follows the equation and Model B follows the equation . True or False: In Model B (), the value of remains constant regardless of the value of , resulting in a horizontal line on a graph.
Analysis of Fixed and Variable Maintenance Costs
Visual Comparison of Fixed and Variable Billing Models