Section 4.5: Linear Functions

Linear functions are functions whose graphs are straight lines. They have the general form \( f(x) = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.

Example 1

Write the linear function with slope 2 and y-intercept -3.

Function: \( f(x) = 2x - 3 \)

Example 2

Find the slope and y-intercept of \( f(x) = -3x + 7 \).

Slope \( m = -3 \)

Y-intercept \( b = 7 \)

Practice Problems

  1. Write the linear function with slope 4 and y-intercept 1.
  2. Find the slope and y-intercept of \( g(x) = 5x - 2 \).
  3. Graph \( f(x) = x + 3 \) on a coordinate plane.
  4. Determine whether \( h(x) = 2x^2 + 3 \) is linear or not.
  5. Write a linear function passing through points (1,2) and (3,6).