Everything Maths Grade 10

On the same set of axes, plot the following graphs:

1.y= 2 x

2.y=x

3.y=x

4.y= 2x

Use your results to deduce the effect of different values ofmon the graph.

The effect ofm

We notice that the value ofmaffects the slope of the graph. Asmincreases, the gradient of the graph increases.

Ifm > 0 then the graph increases from left to right (slopes upwards).

Ifm < 0 then the graph increases from right to left (slopes downwards). For this reason,mis referred to as the
gradient of a straight-line graph.

The effect ofc

We also notice that the value ofcaffects where the graph cuts they-axis. For this reason,cis known as the
y-intercept.

Ifc > 0 the graph shifts vertically upwards.

Ifc < 0 the graph shifts vertically downwards.

m < 0 m= 0 m > 0

c > 0

c= 0

c < 0

Table 6.1:The effect ofmandcon a straight line graph.

VISIT:

You can use thisPhet simulationto help you see the effects of changingmandc.

152 6.2. Linear functions