basic mathematics image
 basic mathematics image

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:


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


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

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