2.2 Lines, 2.3 Lines, Graphing

Graphing Linear Equations by Finding Intercepts

Steps for Graphing with the Intercept Method

  1. Find the x intercept and the y-intercept.
    • To find an x-intercept let y=0 and solve for x.
    • To find a y-intercept let x=0 and solve for y.
  2. Plot the x-intercept and y-intercept.
  3. Draw the line that connects the intercepts.

Example:   Graph the linear equation 2x-3y = 12

Solution:

 1. Find the x-intercept and the y-intercept.

To find an x-intercept: Let y=0 and solve for x.

2x-3y = 12

2x-3(0) = 12

2x-0 = 12

2x = 12

{2x}/2 = {12}/2

x = 6

The x-intercept of this equation is (6,0)

To find a y-intercept: Let x=0 and solve for y.

2x-3y = 12

2(0)-3y = 12

0-3y = 12

-3y = 12

{-3y}/{-3} = {12}/{-3}

y = -4

The y-intercept of this equation is (0,-4)

2. Plot the x-intercept and the y-intercept.

3. Draw the line that connects the intercepts.

 

Example:   Graph the linear equation y=3x

Solution:

 1. Find the x-intercept and the y-intercept.

To find an x-intercept: Let y=0 and solve for x.

y=3x

0=3x

{0}/3 = {3x}/3

0 = x

The x-intercept of this equation is (0,0)

To find a y-intercept: Let x=0 and solve for y.

y=3x

y=3(0)

y=0

The y-intercept of this equation is (0,0)

Since the x-intercept and the y-intercept are the same point and we need two distinct points to graph a line, we must find another ordered pair that is a solution to the equation.

Let x=1 and find the associated y value. (I chose x=1 but you could choose a different value)

y=3x

y=3(1)

y=3

Another ordered pair on the graph is (1,3)

2. Plot the x-intercept and the y-intercept.

3. Draw the line that connects the intercepts.

Example: Graphing a linear equation with intercepts.

Example: Graphing a linear equation with intercepts.

Example: Graphing a linear equation with intercepts.