# How to do linear functions: 8 steps (with pictures)

Some of the most important functions are linear: they have constant rates of change and are therefore graphed with a straight line. You can draw the line if you know at least two points, but it is better to choose 3, that way you can make sure you have not made a mistake. Do you need to work with linear functions? Start with step 1.

## Steps

### Method 1 of 2: Method 1: Graph Linear Functions in Standard Form

#### Step 1. Recognize the standard form of a linear function

Typically, linear functions are written in the form f (x) = ax + b. The "a" represents the gradient of the line, which gives the rate of change of the dependent variable. This is known as the "slope." The "b" represents the intercept with the Y axis. This is the value of the dependent variable or in other words, the value of the function when X = 0.

• For example, let's say you have the function f (x) = x + 5. This is a linear function in its standard form.

#### Step 2. Find at least two spots

You will know that your graph will have a straight line because you have a linear function, therefore you really only need two points. In general, however, you should find 3 points instead of 2 to check for accuracy.

• In the example above, you may be able to choose -1, 0, and 1 for the values of X. Solve as shown in the image.

#### Step 3. Draw the points

Plot the points in the coordinate system using the values you got from solving the 3 equations.

• In the example above, the chart should look like this.

#### Step 4. Connect the dots

For any 2 points, there is only one way to connect them with a straight line. Use a ruler to connect them with a line. You should note that if you graph 3 points and they do not all fall on the same line, you have made a mistake. Go back and calculate everything again.

• In the example above, your chart should look like this.

### Method 2 of 2: Method 2: Graph linear functions in their non-standard form

#### Step 1. Fix the function to make the Y the subject

If you have a linear function that is not in its standard form, you will need to rewrite it before you can graph it.

• Let's say you have the function 6x - 2y = 4. Move everything but the Y to the left as follows.

• Then divide both sides by -2. Now you have the standard form of a linear function: y = 3x - 2.

#### Step 2. Find at least two spots

You will know that your graph will have a straight line because you have a linear function, therefore you really only need two points. In general, however, you should find 3 points instead of 2 to check for accuracy.

• In the rewritten example above, you may be able to choose -1, 0, and 1 as values for X. Solve as follows.

#### Step 3. Draw the points

Plot the points in the coordinate system using the values you got from solving the 3 equations.

• In the example above, the points should look like this.

#### Step 4. Connect the dots

For any 2 points, there is only one way to connect them with a straight line. Use a ruler to connect them with a line. You should notice that if you graph 3 points and they do not all fall on the same line, you have made a mistake. Go back and calculate everything again.

• In the example above, the chart should look like this.