Math Problem Statement

f(x) = -3x + 5

Solution

The function provided in the image is:

f(x)=3x+5f(x) = -3x + 5

This is a linear function, which can be expressed in the form f(x)=mx+bf(x) = mx + b, where mm is the slope and bb is the y-intercept.

For this function:

  • The slope (mm) is 3-3, which means the line decreases as xx increases (a downward slope).
  • The y-intercept (bb) is 55, indicating that the line crosses the y-axis at the point (0,5)(0, 5).

Would you like to see a graph of this function, or do you have any specific questions about it?

Here are 5 related questions to explore further:

  1. What is the x-intercept of the function f(x)=3x+5f(x) = -3x + 5?
  2. How do we find the slope of a linear function from its equation?
  3. What happens to the graph of f(x)f(x) if the slope changes from 3-3 to 22?
  4. How would the graph look if the y-intercept changes to 2-2?
  5. How can this linear function be used to solve real-world problems?

Tip: The slope in a linear equation tells you how much the output (y-value) changes for a unit increase in the input (x-value).

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Math Problem Analysis

Mathematical Concepts

Linear Functions
Algebra

Formulas

f(x) = mx + b (Linear function)
Slope = -3
Y-intercept = 5

Theorems

Slope-Intercept Form of a Line

Suitable Grade Level

Grades 8-10