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Linear function

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College Algebra

Definition

A linear function is a mathematical function that creates a straight line when graphed. It can be expressed in the form $f(x) = mx + b$, where $m$ represents the slope and $b$ represents the y-intercept.

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5 Must Know Facts For Your Next Test

  1. The slope ($m$) of a linear function indicates its steepness and direction (positive slope means upward, negative means downward).
  2. The y-intercept ($b$) is the point where the line crosses the y-axis.
  3. Linear functions have a constant rate of change, meaning they produce equal differences in output for equal differences in input.
  4. The graph of a linear function is always a straight line.
  5. $f(x) = mx + b$ can also be written as $y = mx + b$, which is known as slope-intercept form.

Review Questions

  • What does the slope ($m$) of a linear function represent?
  • How do you find the y-intercept from the equation of a linear function?
  • Explain why the graph of a linear function is always a straight line.
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