Learn Before
Interpreting the Slope and -Intercept of
The linear equation models a woman's estimated height in inches, , based on her shoe size, . Since the equation is in slope-intercept form (), we can identify the slope as and the -intercept as . In this context, the slope of indicates that the estimated height increases by inches for every unit increase in shoe size. The -intercept of signifies that a hypothetical person wearing a women's shoe size of would have an estimated height of inches. Evaluating the equation for a shoe size of yields a height of inches. To graph this relationship, one can plot the -intercept at and use the slope () to count up units and right unit to find a second point.
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 forensic anthropologist uses the linear equation to estimate a woman's height in inches, , based on her shoe size, . According to this model, what is the meaning of the slope, 2?
A physical therapy clinic uses the model to roughly estimate a female patient's height (, in inches) based on her shoe size (). In this linear equation, the -intercept is . This value represents the estimated height in inches of a hypothetical patient who has a shoe size of ____.
A forensic anthropologist uses the linear equation to estimate a woman's height in inches () based on her shoe size (). Match each component of the equation with its correct interpretation according to this model.
An ergonomics specialist uses the linear model to estimate a woman's height in inches () based on her shoe size (). In this model, the -intercept of 50 represents the estimated height in inches of a woman who has a shoe size of 0.
An ergonomics consultant is preparing a training manual that includes a graph of the height-estimation model . Based on the specific graphing procedure described for this model, arrange the following steps in the correct order to plot the relationship on a coordinate plane.