How to Do Linear Functions
Recognize the standard form of a linear function., Find at least two points., Plot the points., Connect the points.
Step-by-Step Guide
-
Step 1: Recognize the standard form of a linear function.
Linear functions are typically 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 also known as the “slope.” The b represents the y-axis intercept.
It is the value of the dependent variable y or, in other words, f(x) when x =
0.
Say, for example, that you have a function f(x) = x +
5.
This is a linear function in standard form. -
Step 2: Find at least two points.
You know your graph will be a straight line because you have a linear function; therefore, you really need only two points.
In general, though, you should find three points instead, to check for accuracy.
In the example above, you might choose to use
-1, 0, and 1 for your x values.
Solve as shown. , Plot your points on the coordinate system, using the values you got from solving your three equations.
In the example above, your graph would look like this. , For any two points, there is only one way to connect them with a straight line.
Use a ruler to join them with a straight line.
Note that if you graph three points, and they don’t all lie on the same line, then you’ve made a mistake somewhere.
Go back and calculate again.
In the example above, your graph would look like this. -
Step 3: Plot the points.
-
Step 4: Connect the points.
Detailed Guide
Linear functions are typically 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 also known as the “slope.” The b represents the y-axis intercept.
It is the value of the dependent variable y or, in other words, f(x) when x =
0.
Say, for example, that you have a function f(x) = x +
5.
This is a linear function in standard form.
You know your graph will be a straight line because you have a linear function; therefore, you really need only two points.
In general, though, you should find three points instead, to check for accuracy.
In the example above, you might choose to use
-1, 0, and 1 for your x values.
Solve as shown. , Plot your points on the coordinate system, using the values you got from solving your three equations.
In the example above, your graph would look like this. , For any two points, there is only one way to connect them with a straight line.
Use a ruler to join them with a straight line.
Note that if you graph three points, and they don’t all lie on the same line, then you’ve made a mistake somewhere.
Go back and calculate again.
In the example above, your graph would look like this.
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