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

(*x*_{1}, *y*_{1}) and (*x*_{2}, *y*_{2}),

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

**Example**:

Graph the equation *x* + 2*y* = 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:

0 + 2*y* = 7

* y* = 3.5

When *y* = 0, we get:

*x* + 2(0) = 7

* x* = 7

So the two points are (0, 3.5) and (7, 0).

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 = *3*x* + 1.

From the equation, we know that the *y*-intercept is 1, the point (0, 1) and the slope is 3. Graph the point (0, 1) 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