Move the sliders for [math]m[/math] and [math]c[/math] to explore the properties of a straight line graph, otherwise known as a [b]LINEAR GRAPH[/b].[br][br][b]Observations: [br][br][/b][b]1.) [/b]What feature of the [color=#ff0000]red line[/color] does [math]c[/math] represent?[br][b]2.) [/b]What do you notice about the [color=#ff0000]red line[/color] as [math]m[/math] gets larger (greater than 1)?[br][b]3.) [/b]What do you notice about the [color=#ff0000]red line[/color] as [math]m[/math] gets smaller (between 0 and 1)?[br][b]4.) [/b]What do you notice when [math]m[/math] is negative?[br][b]5.) [/b]What do you notice when [math]m=0[/math]?[br][b]6.) [/b] What feature of the [color=#ff0000]red line[/color] does [math]m[/math] represent?

Using your observations from above, move the sliders for [math]m[/math] and [math]c[/math] to determine the equation of at least 2 random lines.[br][br][i](Feel free to find the equations of more than just 2 lines. Practice makes perfect!)[/i]

In Mathematics we have a special term to refer to the "steepness" / "slope" of a line. We call it [b]GRADIENT.[br][br][/b]The [b]gradient [/b]of a straight line is denoted by the symbol [math]m[/math] in the linear equation: [math]y=mx+b[/math][br][br]The definition of a gradient is the:[br][br][center][/center][center][i]"Change in vertical distance [math]\left(y\right)[/math] as the horizontal distance [math]\left(x\right)[/math] increases by 1 unit".[br][br][/i][/center]However, we more often us the definition/formula:[br][br][center][math]m=\frac{rise}{run}[/math] or [math]m=\frac{y_2-y_1}{x_2-x_1}[/math][br][br][br][/center]Put your new skills to the test! Try and determine the equation of the following lines![br][br]Pick 2 lines and determine their equation.[br][br]Check that each of your equations are correct by typing them in and seeing if you get a [color=#00ff00]match[/color]. [br][br][i](Two blue points have been given in the top-left which can be moved to help visualize your calculation of "rise" and "run")[/i]