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NATIONAL MATH + SCIENCE INITIATIVEMathematicsTranslations of Linear Functions10 8 6 464222468104 6 8 10LEVELGrade 8 or Algebra 1 in a unit on writing linear equations MODULE/CONNECTION TO AP×Analysis
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How to fill out translations of linear functions

01
To fill out translations of linear functions, follow these steps:
02
Start with the original linear function in the form y = mx + b, where m is the slope and b is the y-intercept.
03
Identify the translation vector. This vector consists of two components: the horizontal shift (represented by h) and the vertical shift (represented by k).
04
To shift the function horizontally, add or subtract the horizontal shift value to the x-values in the function's equation.
05
To shift the function vertically, add or subtract the vertical shift value to the y-values in the function's equation.
06
Simplify the equation by combining like terms, if necessary.
07
The resulting equation represents the translated linear function.

Who needs translations of linear functions?

01
Translations of linear functions are useful to mathematicians, physicists, engineers, and anyone working with mathematical models and equations.
02
These translations help in analyzing the effects of shifting a linear function on its graph and in making predictions based on these shifts.
03
They are also essential in studying transformations in geometry and understanding the concept of slope-intercept form.
04
Students learning algebra and calculus often encounter linear functions and their translations as part of their coursework.
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Translations of linear functions refer to moving the graph of a linear function up, down, left, or right without changing its shape.
Math students or individuals studying linear functions may be required to complete translations of linear functions as part of their coursework.
To fill out translations of linear functions, one must identify the original function, determine the direction of the translation, and apply the correct transformation.
The purpose of translations of linear functions is to understand how moving a graph affects the function's equation and behavior.
Information such as the original function, the direction and amount of the translation, and the new equation of the function must be reported on translations of linear functions.
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