Graph a linear equation

A linear equation in two variables describes a set of ordered pairs whose points lie on a straight line in the coordinate plane. Its graph can be constructed and interpreted from a table of values, slope as the constant rate of change, and the y-intercept, including recognizing that proportional relationships pass through the origin while other linear relationships may not. This scope excludes nonlinear, piecewise, and more advanced analytic treatment of graphs.

Detailed Explanation: Graph a linear equation

A linear equation can be graphed by finding several ordered pairs $(x,y)$ , plotting them, and drawing a straight line through the points.

Example: Graph $y=2x+1$

1. Make a table of values

Choose a few values for $x$ . Substitute each value into the equation.

$x$	$y=2x+1$	Ordered pair
$-1$	$2(-1)+1=-1$	$(-1,-1)$
$0$	$2(0)+1=1$	$(0,1)$
$1$	$2(1)+1=3$	$(1,3)$
$2$	$2(2)+1=5$	$(2,5)$

2. Plot the points

On a coordinate plane:

Plot $(-1,-1)$ .
Plot $(0,1)$ .
Plot $(1,3)$ .
Plot $(2,5)$ .

Remember that an ordered pair $(x,y)$ tells you to move $x$ units left or right, then $y$ units up or down.

3. Draw the line

Use a ruler or a straightedge to draw one straight line through all the points. Extend the line in both directions.

4. Interpret the graph

In $y=2x+1$ :

The number $2$ is the slope. For every increase of $1$ in $x$ , $y$ increases by $2$ .
The number $1$ is the $y$ -intercept. The line crosses the $y$ -axis at $(0,1)$ .

Because the line crosses the $y$ -axis at $1$ , not $0$ , it does not pass through the origin. Therefore, this is not a proportional relationship. A proportional relationship has the form $y=kx$ and always passes through $(0,0)$ .

Learn by doing: Graph a linear equation

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Slope - Find Equivalent - Slope Y Intercept Form to Graph

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