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