Set up the equation of a straight line: formula & examples

You already got to know linear functions in school. Their function equation can be determined in many different ways. In this article, you will learn exactly that. You will learn how to set up the equation of a linear function.

Set up the equation of a straight line – structure

Before we can start setting up the equation of a straight line, let’s first look at what a linear function is and what its functional equation looks like.

The graph of a linear function is always one Just. Therefore, the functional equation of a linear function is also called line equation designated.

y-intercept t

First, let’s look at what exactly the y-intercept is.

The figure shows an example of the y-intercept of a linear function.

incline m

In addition to the y-intercept, the slope of a linear function is of great importance.

The slope of a line can be less than 0, equal to 0, or greater than 0. The course of the graph depends on the slope:

• : The line rises. The graph of the function runs from bottom left to top right (Figure 2).

• : The straight line runs parallel to the x-axis. This type of function will also constant function called.

• : The straight falls. The graph of the function runs from top left to bottom right (Figure 3).

In the figure you can see the slope triangle, the two points and and the slope angle.

Figure 4: Calculate slope

Now that you know all the important terms of the linear function, let’s look at how the equation of a linear function can be set up with different specifications.

Set up the equation of a straight line with two points

You can set up the equation of a line for a linear function given two points and the line.

The procedure for setting up the equation of a straight line from two points is always the same:

1. Calculate the slope using the formula
2. Substituting the slope m and a point into the general equation of a straight line
3. Calculate y-intercept t
4. Specify the equation of the line

Let’s take a look at this procedure with an example.

Set up the equation of a straight line with a point and the y-intercept t

You can also set up the equation of a line for a linear function given the y-intercept t and a point on the line.

Here, too, there is a certain procedure:

1. Inserting the y-intercept t into the general equation of a straight line
2. Calculate the slope m
3. Specify the equation of the line

You can understand the procedure again using an example.

Set up the equation of a straight line with a point and slope m

You can set up the equation of a line for a linear function given the slope m and a point on the line.

You can do this as follows:

1. Inserting the gradient m into the general equation of a straight line
2. Calculate the y-intercept t by inserting the point
3. Specify the equation of the line

To understand this better, you can look at the example.

We want to look at this again with an example.

In some cases, the slope is not given directly, but must first be determined before the straight line equation can be calculated. Let’s look at these cases one by one.

Determining the slope – parallel line

Sometimes it is the case that you should set up the functional equation of a straight line that runs through a certain point and parallel to another straight line.

The following example shows you how this helps you to solve tasks.

Determining the slope – vertical line

But sometimes you also have to set up the functional equation of a straight line that runs through a certain point and perpendicular to another straight line.

How does that look when applied to a concrete example?

In some tasks, you first have to calculate the slope from the slope angle before you can set up the straight line equation.

Determine straight line equation from function graph

You can also determine an equation of a straight line using the function graph of the linear function.

All you have to do is determine the y-intercept from the graph and the slope using two suitable points.