Graphing linear equations

Before graphing linear equations, make sure you understand the concepts of graphing slope since it is very similar.

The standard form of a linear equation is y = mx + b

m is the slope. b is the y-intercept (the y-intercept is a point on the y-axis)

Follow the following guidelines to graph a linear equation:

Method 1

Step #1:

Put the y-intercept on the coordinate system.

Step #2:

Starting from the y-intercept, use the slope to locate one more point on the coordinate system

Step #3:

Draw a line between the y-intercept and the other point

Example #1:

Graph y = (4/3)x + 2

Step #1:

Here m = 4/3 and b = 2. Put 2 on the coordinate system. The graph is below and the y-intercept is shown with a red dot.

Step #2:

Starting from the 2, go up 4 units (you end up at 6, where the black dot is) and over 3 units (The new point is shown with a blue dot)

Notice that we move to the right. We always move to the right!

Step #3:

Draw a line between the red dot and the blue dot. See below:

Graphing linear equations
Example #2:

Graph y = (-4/3)x + 2

Same problem with the exception that the slope is negative.

Step #1 stays the same.

In step #2, you go down 4 units instead of going up. We always go down when the slope is negative, but again we still move to the right

In step #3, after you go down 4 units and move to the right 3 units, the point will be located at (3, -4)

Draw a line between that point and the red dot.

Example #3:

Graph y = x − 2

Rewrite the equation as y = 1x + -2

Here m = 1 and b = -2. Repeat step #1 through #3

Method 2

Method 2 consists of looking for points, at least 2 or 3, plotting them, and drawing a straight line between them

It is common practice to look for the y-intercept, x-intercept, and any other point by letting x be anything and solve for y

Example #4:

Graph y = 2x + -4


When x = 0, y = 2 × 0 + -4 = 0 + -4 = -4 ( Notice that x is always zero when a point is on the y-axis)

The point is (0, -4) shown with a green dot


When y = 0, 0 = 2x + -4 ( Notice that y is always zero when a point is on the x-axis and x-intercept is a point on the x-axis)

So 0 = 2x + -4

0 + 4 = 2x + -4 + 4

4 = 2x

4/2 = (2/2)x

2 = x

The point is (2, 0) shown with a brown dot

At this point, you could make the graph with these 2 points when graphing linear equations, but it will not hurt to get one more

So as we said, let x be anything, say 4, then y = 2 × 4 + -4 = 8 + -4 = 4

The third point is (4, 4) shown in red. The graph is shown below

Graphing linear equations
The two methods above are used when graphing linear equations. Study them carefully!

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