Create the following construction of a slope triangle. Afterwards, use your construction in order to work on the following tasks.

[table][br][tr][td]1.[/td][td][icon]/images/ggb/toolbar/mode_slider.png[/icon][/td][td]Create two sliders for m and b. [br][u]Hint[/u]: Use the default values for the slider interval of -5 to 5.[/td][/tr][tr][td]2.[/td][td][/td][td]Enter the equation of a line [code]y = m*x + d[/code] into the Algebra Input and press the Enter key.[/td][/tr][tr][td]3.[/td][td][icon]/images/ggb/toolbar/mode_intersect.png[/icon][/td][td]Create the intersection point of the line and the y-axis.[br][u]Note[/u]: The name of the intersection point is A.[/td][/tr][tr][td]4.[/td][td][icon]/images/ggb/toolbar/mode_parallel.png[/icon][/td][td]Create a line through point A that is parallel to the x-axis.[/td][/tr][br][tr][td]5.[/td][td][icon]/images/ggb/toolbar/mode_pointonobject.png[/icon][/td][td]Create a point B on the parallel line.[br][/td][/tr][br][tr][td]6.[/td][td][icon]/images/ggb/toolbar/mode_orthogonal.png[/icon][/td][td]Create a line through point B that is perpendicular to the x-axis.[/td][/tr][tr][td]7.[/td][td][icon]/images/ggb/toolbar/mode_intersect.png[/icon][/td][td]Intersect these two new lines.[br][u]Note[/u]: The name of the intersection point is C.[/td][/tr][br][tr][td]8.[/td][td][icon]/images/ggb/toolbar/mode_polygon.png[/icon][/td][td]Draw the slope triangle ABC.[/td][/tr][br][tr][td]9.[/td][td][/td][td]Change the names of the two legs of the slope triangle to Δy and Δx.[br][/td][/tr][tr][td]10.[/td][td][/td][td]Show [i]Name & Value[/i] of the legs of the slope triangle by changing the [i]Labeling [/i]setting on tab [i]Basics [/i]of the Properties dialog. [/td][/tr][br][/table]

Change the values of the sliders m and b, so that you can successively explore the following lines:[br] (1) y = 2x + 1[br] (2) y = 3x - 2[br] (3) y = -x + 2[br][br][b]Task 1[/b]:[br]For each of the lines above, move point B and write down the values of Δy and Δx for at least four different slope triangles.[br][br][u]Note[/u]: Two of your slope triangles should be on the right and two on the left side of the y-axis.[br][br][b]Task 2[/b]: [br]For each of your slope triangles, calculate the ratio of its two legs [math]\frac{\Delta y}{\Delta x}[/math] and compare the four resulting values for each line.[br]