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

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

In this video, you will see how to graph both horizontal and vertical lines:

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]

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]

Objective 4