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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

( x 1 , y 1 ) and ( x 2 , y 2 ) ,

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

Example 1:

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.

Math diagram

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

Example 2:

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.

Math diagram

Horizontal and vertical lines have extra simple equations.

Example 3:

Horizontal line: y = 3

Vertical line: x = 2

Math diagram

 

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