### Chap 12 (ICT Investigation 2) Introduction to Linear Graphs

In pairs, you are going to investigate the change of the "m" in the linear equation "y = mx + c" to find out what it is.

Instructions:
2. Open the file, you will see 2 lines.
• The black line that represents the equation y = x is fixed (it will not move) whereas the move line moves as you drag the slider.
• The equations of the line are displayed on the left panel.

3. Drag the slider (on top) to change the value of n (for the pink line) to 3, 2, 1, 0, -1, -2.

1. Describe the 'relationship' between the pink line and the 2 other lines?
2. Does the orientation of the line change as we drag the slider?
3. What happens to the equation of the blue line as you drag the slider to the different numbers?
4. Make a link between the position of the blue line and the equation.

1. 1.The similarity is the both lines are in a same-interval basis.
2.The line rotates.
3. The blue line remains constant, only the equation changes.For example, if the m value is 2 then the equation will be:b:y=-2x
4. Regardless of the equation the blue line stays at the same position only does the blue line rotate.

2. 1•Describe the 'relationship' between the blue line and the 2 other lines?
The lines intersect at the origin.

2•Does the orientation of the line change as we drag the slider?
The orientation of the lines change as we drag the slider, pivoting around the origin.

3•What happens to the equation of the blue line as you drag the slider to the different numbers?
The equation of the blue line would change according to the number on the slider. For example, y = -3x, the equation on the slide would be m=-3.

4•Make a link between the position of the blue line and the equation.
As the equation decreases, the blue line pivots around the origin, moving from 1st and 3rd quadrant(positive) to 2nd and 4th quadrant.

3. 1. The blue line is equal to 'y=x' when m is equal to 1.

2. The orientation of the line changes.

3. If we drag the slider to a negative number, the coefficient of the equation would be negative too. The coefficient of the equation is actually equivalent to 'm'. Thus, if we drag the slider to a positive number, the coefficient would be positive.

4. The equation has actually something to do with the elevation of the blue line. If 'm' is equal to a negative number, the blue line would point downwards, from the second quadrant to the fourth quadrant. If 'm' is equal to a positive number, then the blue line would be pointing downwards from the first quadrant to the third quadrant.

Poon Wai Kit (19)

4. 1) The lines intersect at the origin
2) Yes, the line rotates around the origin as the number on the slider changes.
3) It changes. When m=3, The equation will be y=3x. The coefficient will be the same value as m.
4) When there is a negative equations, the blue line will be in the 2nd and 4th quadrant. If the equation is positive, the blue line will be in the 1st and 3rd quadrant

5. 1) The lines intercept each other at the origin of the axis (the lines are also equal when m=1)
2) Yes, the line will rotate around the origin when the value of m changes (the line will never not intercept the origin
3) The coefficient of the equation will always be equal to the value of m regardless of what happens
4) The blue line will move from cutting across the 1st and 3rd quadrant (when m>0) to cutting across the 2nd and 4th quadrant (when m<0) (it will rotate around the origin, cutting across quadrants)

6. 1)They intersect at the origin.
2) Yes it does.
3) when u drag the slider to the right the blue line's value increases and when dragged the other way, it decreases.
3) The equation depends on the orientation of the line.