Graphing Linear Equations
Move the sliders for and to explore the properties of a straight line graph, otherwise known as a LINEAR GRAPH.
Observations:
1.) What feature of the red line does represent?
2.) What do you notice about the red line as gets larger (greater than 1)?
3.) What do you notice about the red line as gets smaller (between 0 and 1)?
4.) What do you notice when is negative?
5.) What do you notice when ?
6.) What feature of the red line does represent?
Using your observations from above, move the sliders for and to determine the equation of at least 2 random lines.
(Feel free to find the equations of more than just 2 lines. Practice makes perfect!)
Visualizing the Gradient (m) of a Straight Line
In Mathematics we have a special term to refer to the "steepness" / "slope" of a line. We call it GRADIENT.
The gradient of a straight line is denoted by the symbol in the linear equation:
The definition of a gradient is the:
"Change in vertical distance as the horizontal distance increases by 1 unit".
However, we more often us the definition/formula:or
Put your new skills to the test! Try and determine the equation of the following lines! Pick 2 lines and determine their equation. Check that each of your equations are correct by typing them in and seeing if you get a match. (Two blue points have been given in the top-left which can be moved to help visualize your calculation of "rise" and "run")