In the sheet, the equation of the line is [math]y=mx+c[/math]. The values of coefficients m and c are initially set to [math]m=\frac{1}{2}[/math] and [math]c=2[/math]. You can change these values by moving the dot on the green slider bars. [br][br]The value of c just shifts the line position up and down but the angle of the line does not change. [br][br]The value of m will change the angle of the line. As m becomes a bigger positive number, the line becomes more vertical. As m gets closer to zero, the line becomes more horizontal. When m=1, the line is at 45 degrees. When m is negative, the line angle is pointing down towards the right hand side.[br][br]You can move points X1 and X2 along the x-axis. This will also move points A and B on the line. The corresponding points on the y-axis are Y1 and Y2.[br][br]The red arrows show the distances in the horizontal and vertical direction between points A and B. The horizontal distance is [math]\Delta x=x_2-x_1[/math]. The vertical distance is [math]\Delta y=y_2-y_1[/math].[br][br]See that the coefficient m is given by [math]m=\frac{\Delta y}{\Delta x}=\frac{\left(y_2-y_1\right)}{\left(x_2-x_1\right)}[/math].[br]Likewise, the value m tells how much the y value changes when the x-value changes, going from point A to point B.[br]Take example of [math]y=\frac{1}{2}x+2[/math] where [math]m=\frac{1}{2}[/math]. When [math]x=-1[/math], then y is: [math]y\left(-1\right)=\frac{1}{2}\left(-1\right)+2=1.5[/math]. Then the point on the graph for this point is [math]\left(x,y\right)=\left(-1,1.5\right)[/math][br][br]