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How to find the gradient of a line through the origin and another fixed point.

This topic is part of the TCS FREE high school mathematics 'How-to Library'. It shows you how to find the gradient of a line through the origin and another fixed point.
(See the index page for a list of all available topics in the library.) To make best use of this topic, you need to download the Maths Helper Plus software. Click here for instructions.


The gradient 'm' of a line segment between two points: (x1,y1) and (x,y) is defined as follows:

It the point (x1,y1) is the origin: (0,0), then the gradient of the line segment can be defined as follows:

Example: Find the gradient of the line through the origin and the point (3,4).

Solution:  m = y/x = 4/3. (Or 1.333333... as a decimal fraction.)

This is illustrated graphically on the diagram below. The origin is the red dot at the lower left. The line segment joining the origin to the other red dot at (3,4) has gradient m = 4/3


Maths Helper Plus can find the gradient (and the equation) of a straight line joining the origin (0,0) to a point (x,y). It will calculate the gradient and show the working steps and display a labelled diagram.  

Step 1 Download the free support file... We have created a Maths Helper Plus document containing the completed example from this topic. You can use this to practice the steps described below, and as a starting point for solving your own problems.

File name:  'Gradient from origin to point.mhp'   File size: 8kb
Click here to download the file.

If you choose 'Open this file from its current location', then Maths Helper Plus should open the document immediately. If not, try the other option: 'Save this file to disk', then run Maths Helper Plus and choose the 'Open' command from the 'File' menu. Locate the saved file and open it. If you do not yet have Maths Helper Plus installed on your computer, click here for instructions.

Step 2  Display the parameters box

Press the F5 key to display the parameters box:


The coordinates of the (x,y) point is entered into the two edit boxes 'A' and 'D', as follows:

x = A, and y = D.

To calculate the gradient of the line segment from the origin to the point (x,y) and the equation of the straight line joining the points, enter the coordinates of (x,y) into the edit boxes.


To enter the coordinates, click on the 'A' edit box with the mouse, then type the x coordinate. Now click on the 'D' edit box and type the y coordinate. Click the 'Update' button to update the calculations and the labelled diagram.


Step 3  Adjust the scale of the labelled diagram

If your point (x,y) is off the graphing area of the screen, the scale needs to be reduced. In this case, briefly press the F10 key enough times until the two plotted points are seen.


You can also make the diagram bigger by holding down 'Ctrl' while you press F10.


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