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 $y=mx+b$ 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 $y+3x=5$ .

Show Solution

First, solve

y + 3 x = 5

$y+3x=5$ for y, then the equation will look familiar and you can create a table of ordered pairs.

$\begin{array}{r}y+3x-3x=5-3x\\y=5-3x\end{array}$

Evaluate $y=5–3x$ for different values of x, and create a table of corresponding x and y values.

x values	$5–3x$	y values
$0$	$5–3(0)$	$5$
$1$	$5–3(1)$	$2$
$2$	$5–3(2)$	$−1$
$3$	$5–3(3)$	$−4$

Plot the ordered pairs (shown below).

$(0,5)$

$(1,2)$

$(2,−1)$

$(3,−4)$

Graph showing the point (0,5), the point (1,2), the point (2,-1), and the point (3,-4).

Draw a line through the points to indicate all of the points on the line.

Answer

Graphing Linear Equations (9)

In this video, you will see another example of graphing by using a table:

Horizontal and Vertical Lines

The linear equations $x=2$ and $y=−3$ 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 $x=2$ as $x=0y+2$ and think of $y=−3$ as $y=0x–3$ .

Example

Graph $y=−3$ .

Show Solution

x values	$0x–3$	y values
$0$	$0(0)–3$	$−3$
$1$	$0(1)–3$	$−3$
$2$	$0(2)–3$	$−3$
$3$	$0(3)–3$	$−3$

Write $y=−3$ as $y=0x–3$ , and evaluate y when x has several values. Or just realize that $y=−3$ means every y value will be $−3$ , no matter what x is.

$(0,−3)$

$(1,−3)$

$(2,−3)$

$(3,−3)$

Plot the ordered pairs (shown below).

Graph with the point (1,-3), the point (2,-3), and the point (3,-3).

Draw a line through the points to indicate all of the points on the line.

Answer

Graphing Linear Equations (11) Notice that $y=−3$ graphs as a horizontal line.

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

Objective 4