Straight Line Graphs and Equations 1 - Gradient and Intercept

This applet investigates straight line graphs, gradients (slopes) and y-intercepts, and equations in gradient-intercept (slope-intercept) form: y = mx + c

Author and programmer: Ron Barrow

UK - Years 8-11, KS3, KS4, Foundation and Higher GCSE Mathematics - Algebra and Graphs
US - Grades 9-10, Algebra and Geometry (Graphs)

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Instructions below    Waldomaths video    Waldomaths video    Waldomaths video    See also:   Straight Line Graphs 2    Coordinate Geometry

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How to Use this Applet

The purpose of this applet is to investigate the relationships between different features of straight lines. For any straight line the following features are all inter-related:
 • the gradient
 • the y-intercept
 • the equation of the line
 • the graph of the line
You can show or hide these features by clicking the boxes at the bottom.
By moving the top two sliders on the bottom right you can change the gradient of the line. The gradient is written as a fraction if it is not an integer. The top slider changes the numerator and the second changes the denominator of the gradient fraction.
The bottom slider changes the y-intercept of the line - the point where it crosses the y-axis. Here the intercept is always an integer.

The equation of the line is visible at the top right.
There is a green triangle on the screen which can be moved by dragging the red vertices with your mouse. This triangle displays its own height and width. You can use this triangle to investigate and draw gradients.
Pressing the "Reset" button takes you back to the start position.
Clicking "Random" draws a random line for you, and this will help you test your understanding of this topic. You can make the random line easier to understand if you tick the "integer gradient" box and/or the "positive gradient" box beforehand.
There is a selection of investigations at the top of the screen. Choose one of the items from the drop-down menu and the screen will set up for that investigation.
You can learn a great deal about straight lines by playing around with this program. Enjoy!