Skill: 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 $(0,0)$.