### Chap 12 (ICT Investigation) Study Notes (p9-p11)

Variation in the value of m with the value of c kept constant

Increase the value of m. What do you observe about the straight line?
As m increases, the slope becomes steeper.

Now decrease the value of m. What do you observe about the straight line?
As m decreases, the slope becomes more gentle.

Now further decrease the value of m till it comes negative. What do you observe about the straight line?
The line continues to "go down": Now the axis points from top left corner towards bottom right corner. (opposite direction).

Now set the value m = 0. What do you observe about the straight line?
When m becomes zero, the line becomes the horizontal line that overlaps with the x axis.

Variation in the value of c with the value of m kept constant

Increase the value of c. What do you observe about the straight line?
The straight line 'moves' up, and it remains parallel to the original line.

Now decrease the value of c. What do you observe about the straight line?
The straight line 'moves' up, and it remains parallel to the original line.

What happens to the straight line when the value of c = 0?
The straight one passes through the origin.

Now summarize on your own the effect of m and c on a straight line with equation y = mx + c

c is the vertical intercept that tells us where the graph will intersect/ cut the y axis whereas m is the gradient that tells us the orientation of the graph (steep/ gentle, pointing upwards/ downwards).

What happen if now we have two lines having the same gradient?
Consider y = 2x + 4 and y = 2x - 1

The two lines will be parallel to each other.

What happen if now we have two lines having the same y-intercept?
Consider y = 2x + 1 and y = -4x + 1

The two line will cut the y-axis at y = 1

What is the general form of a horizontal straight line?
Why is it in that particular form?
The general form is y = c when c is the 'y'-intercept
i.e. when the line is parallel to the x axis.

What is the general form of a vertical straight line?
What is it in that particular form?
The general form is x = n where n is the 'x'-intercept
i.e. when the line is parallel to the y axis.