### Chap 12 (ICT Investigation 1) Introduction to Linear Graphs

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

Instructions:

2. Open the file, you will see 3 lines.
• The 2 black lines represent equations y = 2x + 5 and y = 2x -2 while the pink line can "move".
• 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 pink line as you drag the slider to the different numbers?
4. Make a link between the position of the pink line and the equation.

1. 1. As 'n' increases from -2 to 3, the pink line moves closer to the "y= 2x+5" black line.

2. The line stays the same no matter what the number on the slider is changed. The only difference is that its coordinates change when the number on the slider is changed.

3. The constant in the pink line's equation is equal to the number (n) on the slider, meaning that the equation of the pink line is "2x+n".

4. As the equation increases, the pink line moves towards the second and third quadrant. However, as the equation decreases, the line moves towards the first and fourth quadrant.

1. Poon Wai Kit (19)

2. 1. The lines are parallel to each other.
2. The lines remain the same except for the change in the coordinates.
3. The equation of n(pink line) and c is changed.For example, if the n value is 1, then c value is 2x+1.
4. As the equation increases the pink line moves downwards towards the 1st and 4th quadrant but if the equation increases the pink line moves upwards towards 2nd and 3rd quadrant. This is because of the change in the equation.

3. 1•Describe the 'relationship' between the pink line and the 2 other lines?
The lies are parallel to one another.

2•Does the orientation of the line change as we drag the slider?
The orientation of the lines do not change as we drag the slider.

3•What happens to the equation of the pink line as you drag the slider to the different numbers?
The equation of the pink line would change according to the number on the slider. For example, y = 2x + 3, the equation on the slide would be n=3.
4•Make a link between the position of the pink line and the equation.
As the equation decreases, the pink line moves lower, along the y axis.

4. Great explanation with great ideas, graph is the best way to understand the equation. In this blog the main thing is the graph and to get the best answer of linear equation you have to draw a graph.linear equation

5. 1) They are parallel to one another.
2) The orientation of the lines do not change, but the coordinates do.
3) The equation of the pink line will change. When n=-1, the equation is y=2x-1.
4) As the equation decreases, the pink line will move closer to the black parallel lines.

6. 1) They are al parallel to each other, wherever the pink line moves.
2) They do not change
3) If I move the pink line its equation will change. like n= -2, then the y= 2x-2
4) As the equation of the pink line decreases, the line will move closer to the black lines even more

7. 1) All the lines are parallel to each other (it does not matter if the pink line move)
2) No, the orientation of the line does not change
3) When the line moves, the equation of the pink line will change (in relation to the x axis)
4) As value of the variable of the equation reaches 0, it will move closer and closer to the center of the axis (eventually slicing through the center of the axis)

8. 1)As u move the line towards the line y=2x+5 and when you move the line towards the left the line moves towards y=2x-2.
2)No it does not.
3) It will increase and decrease.
4) The equation of the pink line depends on the position of it.

9. 1) The pink line is parallel to the 2 other lines.
2) No, the orientation of the line remains the same.
3) The pink line will be situated at n on the y axis, as u shift n. The equation of the pink line is 2x+n.
4) As the equation increases, the pink line's intersection at the y axis will increase too. As the equation decreases, the pink line's intersection at the
y axis will also decrease too.

1. Equation: Y=m (gradient) x + C (The constant term is the y intersect.)

10. 1. The lines are parallel to each other.
2. The lines remain the same except for the change in the coordinates.
3. The equation of n(pink line) and c is changed.For example, if the n value is 1, then c value is 2x+1.
4. As the equation increases the pink line moves downwards towards the 1st and 4th quadrant but if the equation increases the pink line moves upwards towards 2nd and 3rd quadrant. This is because of the change in the equation.

11. 1) The lines are always parallel no matter where the pink line is
2) The line does not change, only the position of it.
3) The equation is 2x + n. EG. if n=5, the equation is 2x + 5. If n = -3.5, the equation is 2x + (-3.5) = 2x - 3.5
4) As the equation moves, the intersection of the pink line at the y axis will be the same as the n value.