Math Problem Statement

Is the function y = -9x + 10 linear or nonlinear?

Solution

The function provided is y=9x+10y = -9x + 10.

This is a linear function because it can be written in the form y=mx+by = mx + b, where mm and bb are constants. In this case, m=9m = -9 and b=10b = 10, and the variable xx 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:

  1. What are the slope and y-intercept of the function y=9x+10y = -9x + 10?
  2. How do we graph a linear equation like y=9x+10y = -9x + 10?
  3. What is the difference between a linear and nonlinear function?
  4. How do changes in the coefficient mm affect the steepness of the graph?
  5. 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