How to find the gradient of a line joining two fixed
points.

This topic is part of the
TCS FREE high school mathematics 'Howto Library'.
It shows you how to find the gradient of a line joining two fixed
points.
(See the index page
for a list of all available topics in the library.)Â To
make best use of this topic, you need to download the Maths Helper Plus
software. Click
here for instructions. 
Theory:
Consider two fixed points: (x_{1},y_{1})
and (x_{2},y_{2}), joined by a straight line:
Starting at (x_{1},y_{1}) on the left, then moving to the right along
the line to (x_{2},y_{2}), we measure the change in 'x', and
the change in 'y'.
The change in 'x'Â =Â x_{2}  x_{1}
while the change in 'y' =Â Â y_{2}  y_{1}
These quantities are shown on the following diagram:
The gradient 'm' of the line segment is defined as follows:
The Greek capital letter 'Delta' : D
is often used in mathematics to mean a change in some quantity. So the
gradient definition can be written like this:
To measure the change in 'x' and 'y' between the two points , we draw a right triangle beneath the graph. The length of the
vertical leg is: (y_{2}y_{1}), and the
horizontal leg has length (x_{2}x_{1}).
In the diagram below, (x_{1}, y_{1}) = (2, 3) and (x_{2},
y_{2}) = (6, 8)...
Â So the gradient of this line segment is:Â
Method:
Maths Helper Plus can find the
gradient of a straight line between two points. It will calculate the gradient showing the working steps. It also displays a labelled diagram.
Â
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:Â 'Gradient between two points.mhp'Â Â File size: 4kb
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 2Â Display
the parameters box
Press the F5 key to display the
parameters box:
Â
The coordinates of two (x,y)
points are entered into the four edit boxes 'A', 'B', 'C' and 'D', as follows:
x_{1} =
A,Â y_{1} = D,Â x_{2} = B, and y_{2} = X.
To
find the gradient of the straight line through two points, enter the coordinates of two points
into the edit boxes.
Â
To
enter the coordinates, click on the 'A' edit box with the mouse, then type the x_{1}
coordinate. Now click on the 'D' edit box and type the y_{1}
coordinate. Continue until the four coordinates are entered, then click the
'Update' button.
Â
Step 3Â Adjust
the scale of the labelled diagram
If the points lie 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.
Â
You can make the diagram bigger by
holding down 'Ctrl' while you press F10.
Â
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