More Graphing Linear Equations With a Table and Vertical and Horizontal Lines
Learning Objectives
Graph Linear Equations in Different Forms
Solve for y, then graph a two-variable linear equation
Graph horizontal and vertical lines
Solve for y, then graph a linear equation
The linear equations we have graphed so far are in the form [latex]y=mx+b[/latex] where m and b are real numbers. In this section we will graph linear equations that appear in different forms than we have seen.
Example
Graph the linear equation [latex]y+3x=5[/latex].
Show Solution
First, solve [latex]y+3x=5[/latex] for y, then the equation will look familiar and you can create a table of ordered pairs.
Evaluate [latex]y=5–3x[/latex] for different values of x, and create a table of corresponding x and y values.
x values
[latex]5–3x[/latex]
y values
[latex]0[/latex]
[latex]5–3(0)[/latex]
[latex]5[/latex]
[latex]1[/latex]
[latex]5–3(1)[/latex]
[latex]2[/latex]
[latex]2[/latex]
[latex]5–3(2)[/latex]
[latex]−1[/latex]
[latex]3[/latex]
[latex]5–3(3)[/latex]
[latex]−4[/latex]
Plot the ordered pairs (shown below).
[latex](0,5)[/latex]
[latex](1,2)[/latex]
[latex](2,−1)[/latex]
[latex](3,−4)[/latex]
Draw a line through the points to indicate all of the points on the line.
Answer
In this video, you will see another example of graphing by using a table:
Horizontal and Vertical Lines
The linear equations [latex]x=2[/latex] and [latex]y=−3[/latex] only have one variable in each of them. However, because these are linear equations, then they will graph on a coordinate plane just as the linear equations above do. Just think of the equation [latex]x=2[/latex] as [latex]x=0y+2[/latex] and think of [latex]y=−3[/latex] as [latex]y=0x–3[/latex].
Example
Graph [latex]y=−3[/latex].
Show Solution
x values
[latex]0x–3[/latex]
y values
[latex]0[/latex]
[latex]0(0)–3[/latex]
[latex]−3[/latex]
[latex]1[/latex]
[latex]0(1)–3[/latex]
[latex]−3[/latex]
[latex]2[/latex]
[latex]0(2)–3[/latex]
[latex]−3[/latex]
[latex]3[/latex]
[latex]0(3)–3[/latex]
[latex]−3[/latex]
Write [latex]y=−3[/latex] as [latex]y=0x–3[/latex], and evaluate y when x has several values. Or just realize that [latex]y=−3[/latex] means every y value will be [latex]−3[/latex], no matter what x is.
[latex](0,−3)[/latex]
[latex](1,−3)[/latex]
[latex](2,−3)[/latex]
[latex](3,−3)[/latex]
Plot the ordered pairs (shown below).
Draw a line through the points to indicate all of the points on the line.
Answer
Notice that [latex]y=−3[/latex] graphs as a horizontal line.
In this video, you will see how to graph both horizontal and vertical lines:
Licenses and Attributions
All rights reserved content
Graphing Horizontal and Vertical Lines (L8.6). Authored by: mathispower4u. Located at: https://youtu.be/2A2fhImjOBc. License: All Rights Reserved. License Terms: Standard YouTube License
Ex 3: Graph a Linear Equation in Standard Form Using a Table of Values. Authored by: mathispower4u. Located at: https://youtu.be/6yL3gfPbOt8. License: All Rights Reserved. License Terms: Standard YouTube LIcense
Notice that [latex]y=−3[/latex] graphs as a horizontal line.