# X and Y Intercepts

Image Source: http://www.geograph.org.uk

In this lesson we look at Straight Line Graphs in relation to X and Y Intercepts.

This includes understanding what “Intercepts” are in terms of their similarity to Road and Rail Crossings and Intersections.

We then look at how to read Intercepts off Graphs, as well as finding Intercepts for a Straight Line Equation.

We then show how easy it is to make a sketch graph of a Straight Line using the values of its X and Y Intercepts.

First we need to understand exactly what “X and Y Intercepts” are, and how to read them off a graph.

X-Intercept and Y-Intercept

If we think of “Intercepts” as being like Intersections on roads, this might help us to grasp the concept.

In the opening photo for this lesson we have the Intersection of a Train Line with a Main Road.

Here is a map showing where a train line near where Passy works intersects with two main roads.

Image Copyright 2013 by Passy’s World of Mathematics

If we think of the Train Line as being our Straight Line, and the Two Main Roads being the “X-axis” and the “Y-axis”; then we have the following situation:

Image Copyright 2013 by Passy’s World of Mathematics

Note that in Coordinate Geometry the meeting points are called “Intercepts” rather than “Intersections”.

So when examining graphs, think of the X and Y Axises as being two main roads. (It might even help to draw over the top of them in different colours).

Think of the Straight Line as being either a Train Line, (or another major road), that intersects (or crosses over) the two main X and Y Roads.

The Point where the Straight Line crosses over the X-Axis is called the “X-Intercept”

The Point where the Straight Line crosses over the Y-Axis is called the “Y-Intercept”

X-Intercept and Y-Intercept Examples

Image Copyright 2013 by Passy’s World of Mathematics

Note that we can specify either the Axis Value of an Intercept, or its specific (x,y) coordinates.

Here is a second example to try yourself, the answer is shown further down the page.

Image Copyright 2013 by Passy’s World of Mathematics

Here is the Answer to Example One.

Image Copyright 2013 by Passy’s World of Mathematics

X-Intercept and Y-Intercept from Graphs Videos

This short one and a half minute video shows how to find the Intercepts for a basic Line Graph.

This next video also covers Horizontal and Vertical Lines, which only have one Intercept.

X-Intercept and Y-Intercept from Graphs Worksheet

The following Worksheet can be done as an Online Worksheet.

Questions 1 to 10 are on Y-Intercept, and Questions 11 to 20 are on X-Intercept.

Go to the bottom of the web page to check your answers.

X-Intercept and Y-Intercept from Graphs Worksheet

Calculating X and Y Intercepts from Equations

A lot of times we do not have a Graph of the Straight Line, and only have its Equation.

We could plot some points, and draw the graph, but this is a lot of work.

There is a much faster Algebra Equations Method for Calculating the Intercepts.

With this method we do not have to draw any graphs.

The Algebra Rule works like this:

To find the X-Intercept, substitute y=0 into the equation and solve for x

To find the Y-Intercept, substitute x=0 into the equation and solve for y

A lot of people get confused, and think for the X-Intercept, they should be substituting x=0 !

Try to remember that the substitution is the opposite way around to what you would think.

For the X-Intercept, we substitute y=0 because all points along the X-Axis have a y coordinate of zero.

For the Y-Intercept, we substitute x=0 because all points along the Y-Axis have an x coordinate of zero.

Image Copyright 2013 by Passy’s World of Mathematics

Finding X and Y Intercepts – Example 1

In the following example we use zero substitutions to find the X and Y Intercepts.

Notice that whatever we substitute as zero, ends up as the zero coordinate in the final answer, as shown by the long arrows.

Image Copyright 2013 by Passy’s World of Mathematics

Once we have the two intercepts, drawing a sketch graph is very easy, as shown below.

Simply Plot the Two Intercept values onto a labelled X-Y Grid, and then connect them with a straight line with arrows on each end.

Also write the original Equation of the line onto the Grid.

Image Copyright 2013 by Passy’s World of Mathematics

Finding X and Y Intercepts – Example 2

In the following example we again use zero substitutions to find the X and Y Intercepts.

Complete the partly worked out example below.

(You can then scroll down the page to see the fully worked answer)

Image Copyright 2013 by Passy’s World of Mathematics

Here is the fully worked solution to Example 2.

Image Copyright 2013 by Passy’s World of Mathematics

Complete the Graph for Example 2 using the X-Y Grid Layout below.

Simply Plot the Two Intercept values onto a labelled X-Y Grid, and then connect them with a straight line with arrows on each end.

Also write the Equation of the Line onto the Grid.

(You can then scroll down the page to see the fully worked answer)

Image Copyright 2013 by Passy’s World of Mathematics

Image Copyright 2013 by Passy’s World of Mathematics

Finding X and Y Intercepts Videos

This first video shows how to find the X-Intercept and Y-Intercept using substitution of zero values.

This part of the video starts about two minutes into the video, the beginning is a review of locating the Intercepts on a Straight Line Graph.

This next two and a half minute video, shows how to find the Intercepts, and then goes the next step and Sketches the Straight Line Graph.

X and Y Intercepts Worksheets

This first Worksheet actually contain five sheets of questions with the answers at the bottom of each sheet.

Intercepts Worksheet 1

This second worksheet has graph Sketching Questions, (Questions 15 to 260, with Answers at the end of the sheet.

(Do not do Questions 7 to 14 of this sheet on Gradient Intercept, as we have not covered that work in this lesson).

Intercepts Worksheet 2

X and Y Intercept Online Calculator

Shown above is a great free Online App we can use for finding X and Y Intercepts.

Simply type your line equation into this calculator, Click the “Solve” button, and it will give you the coordinates of your X and Y Intercepts.

Click the following link to access this Intercepts Calculator:

Related Items

Subscribe

If you enjoyed this lesson, why not get a free subscription to our website.

To find out exactly how free subscription works, click the following link:

How Free Subscription Works

If you would like to submit an idea for an article, or be a guest writer on our website, then please email us at the hotmail address shown in the right hand side bar of this page.

If you are a subscriber to Passy’s World of Mathematics, and would like to receive a free PowerPoint version of this lesson, that is 100% free to you as a Subscriber, then email us at the following address:

Please state in your email that you wish to obtain the free subscriber copy of the “X and Y Intercepts”

Feel free to link to any of our Lessons, share them on social networking sites, or use them on Learning Management Systems in Schools.

Our Facebook page has many additional items which are not posted to this website.

These include items of mathematical interest, funny math pictures and cartoons, as well as occassional glimpses into the personal life of “Passy”.

Check it out at the following link:

Help Passy’s World Grow

Each day Passy’s World provides hundreds of people with mathematics lessons free of charge.

Help us to maintain this free service and keep it growing.

Donate any amount from \$2 upwards through PayPal by clicking the PayPal image below. Thank you!

PayPal does accept Credit Cards, but you will have to supply an email address and password so that PayPal can create a PayPal account for you to process the transaction through. There will be no processing fee charged to you by this action, as PayPal deducts a fee from your donation before it reaches Passy’s World.

Enjoy,
Passy