4.2 Graphing Linear Functions
Use tables and equations to graph linear functions.
Parent Functions
A family of functions is a group of
functions with common characteristics.
 Simplest function with these
characteristics is called a parent
function.
 The linear parent function is y = x or
f(x) = x

Linear Equation
Models a linear function
 Variable cannot be raised to a power other
than 1
 y = 2x is linear but y = x2 and y = 2x are not.
 The y-intercept is the y-coordinate of a
point where the graph crosses the y-axis.

Slope-Intercept Form
For linear equations that are not vertical.
 Remember, the slope of a vertical line is
undefined.

Ex: identify the slope and y-intercept for
the linear equation y = 5x – 2
 Slope: 5
 y-intercept: -2

Writing an Equation

What is the equation of the line with a
4
slope of − and y-intercept 7?
5

Plug into slope-intercept form:
◦
◦
4
m=−
5
4
y=- 𝑥
5
and b = 7
+7
From a Graph
Crosses the y-axis at -2 so
b = -2
 Pick two points to find the
slope:
(0, -2) and (1, 0)
m=2
 Write an equation using slope-intercept
form:

◦ y = 2x – 2
From Two Points


Find the equation of the line that passes
through (2,1) and (5, -8)
Use the points to find slope
◦ m = -3
Use slope and one of the points to find b
 y = -3x + b and plug in the point (2, 1)
 1 = -3(2) + b
 1= -6 + b
7=b
 Write the equation

◦ y = -3x + 7
Graphing

What is the graph of y = 2x – 1?
Practice

What is the graph of each linear equation?

y = -3x + 4

y = 4x – 8