In the sheet, the equation of the line is . The values of coefficients m and c are initially set to and . You can change these values by moving the dot on the green slider bars.
The value of c just shifts the line position up and down but the angle of the line does not change.
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.
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.
The red arrows show the distances in the horizontal and vertical direction between points A and B. The horizontal distance is . The vertical distance is .
See that the coefficient m is given by .
Likewise, the value m tells how much the y value changes when the x-value changes, going from point A to point B.
Take example of where . When , then y is: . Then the point on the graph for this point is