How To Graph Linear Equations

Graphing linear equations is one of the basic skills learned in algebra. To get a better grasp on doing this, one needs to have sheets of graphing paper, a ruler and pencil.

Here's a short guide on how you can graph linear equations.

1. Before starting with the graphing paper, simplify the equation that needs to be graphed in the familiar y = mx + b configuration. The y variable stands for the value for y, which is the vertical axis in the graph. The m is also known as the "slope". It's a rise-over-run formula. The x variable stands for the value of x, or the horizontal axis in the graph.

Take this equation for example:

y = 4x + 3

2. Now draw the beginnings of your graph. Draw two perpendicular lines on the graphing paper. The horizontal line is the x axis. The vertical line is the y axis.

3. The first thing that we have to do is to determine the y-intercept. The y intercept is the point on the y axis where the line of your equation crosses. To do this, you have to assume that x is zero, because this is the point on your horizontal axis that intersects the zero on the vertical axis.

For the expression given:

Y = 4 (0) + 3

Y = 3

Therefore, the line would cross at the level of 3 on the y axis or the vertical line. When written as a point, this would read as (0 , 3). The zero corresponds to the value of x, while the 3 is the value of y.

4. Determine the rest of the points of the line. You may do this using two techniques. The first one is using the substitution technique.

a. Simply substitute values for x and solve for y:

Y = 4x + 3

  • If x were equal to 2, y would be 11 (2, 11)
  • If x were equal to 1, y would be 7 (1, 7)
  • If x were equal to -1, y would be -1 (-1, -1)
  • If x were equal to -2, y would be -5 (-2, -5)

Plot these points and draw a line through them. Since this is a linear expression, the tip of the line has to be added with arrow heads. This is to signify that the values on the line stretch to infinity.

b. Use the slope.

The second method involves using the slope of the equation. Again, the slope is rise over run. Rise is the displacement over the y axis while run is the movement along the x axis. Therefore, for the equation:

Y = 4x + 3

The slope is 4. This means that for every 4 units in rise, there is 1 unit of run. For every 4 units you go up, you go to the right by one unit.

Since we already know our y intercept, we can add and subtract accordingly to determine the rest of the points on the line.

The y intercept is at (0,3). The next point would be at (1,7), the point after that would be at (2,11). If you noticed, the points plotted using both techniques are the same. Just determine which one is easier for you to do.

Mathematics is all about practice, so keep graphing to improve your skills. It will not matter which method you prefer to use - substitution or the slope method. But it will be good to learn both concepts, as these might come in handy, especially when answering word problems.


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