Math Problem Statement
Is the function y = -9x + 10 linear or nonlinear?
Solution
The function provided is .
This is a linear function because it can be written in the form , where and are constants. In this case, and , and the variable appears with a power of 1 (i.e., it is not squared, cubed, or involved in any non-linear operations like exponentials or trigonometric functions). Therefore, the function represents a straight line.
Would you like more details or have any questions?
Here are five related questions to explore:
- What are the slope and y-intercept of the function ?
- How do we graph a linear equation like ?
- What is the difference between a linear and nonlinear function?
- How do changes in the coefficient affect the steepness of the graph?
- What types of real-world problems can be modeled with linear equations?
Tip: Linear functions graph as straight lines, while nonlinear functions involve curves or more complex shapes.
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Math Problem Analysis
Mathematical Concepts
Linear Functions
Algebra
Formulas
y = mx + b
Theorems
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Suitable Grade Level
Grades 7-9