# Graphing Linear Equations

The graph of a linear equation in two variables is a line (that's why they call it linear).

If you know an equation is linear, you can graph it by finding any two solutions

$\left({x}_{1},{y}_{1}\right)$ and $\left({x}_{2},{y}_{2}\right)$,

plotting these two points, and drawing the line connecting them.

Example:

Graph the equation $x+2y=7$.

You can find two solutions, corresponding to the $x$-intercepts and $y$-intercepts of the graph, by setting first $x=0$ and then $y=0$.

When $x=0$, we get:

$\begin{array}{l}0+2y=7\\ y=3.5\end{array}$

When $y=0$, we get:

$\begin{array}{l}x+2\left(0\right)=7\\ x=7\end{array}$

So the two points are $\left(0,3.5\right)$ and $\left(7,0\right)$.

Plot these two points and draw the line connecting them.

If the equation is in slope-intercept form or point-slope form, you can also use the slope to help you graph.

Example:

Graph the line $y=3x+1$.

From the equation, we know that the $y$-intercept is $1$, the point $\left(0,1\right)$ and the slope is $3$.  Graph the point $\left(0,1\right)$ and from there go up $3$ units and to the right $1$ unit and graph a second point.  Draw the line that contains both points.

Horizontal and vertical lines have extra simple equations.

Example:

Horizontal line: $y=3$

Vertical line: $x=-2$