Question

David wants to purchase some pens. The pens he likes cost $2 each, not including tax. This is represented by the graph below.

Notice triangle BAC.
Notice triangle BDE.
Explain how the triangles demonstrate that the rate of change is consistent for number of pens purchased and the cost.

Answer 1

The rate of change is always the same for a straight line no matter the points used.

The equation of a straight line is given by:

y = mx + b;

where y, x are variables, m is the rate of change and b is the y intercept.

In triangle BAC:

Rate of change = change in y(cost) / change in x(pens) = (6 - 0) / (3 - 0) = 2

In triangle BDE:

Rate of change = change in y(cost) / change in x(pens) = (8 - 0) / (4 - 0) = 2

The rate of change is always the same for a straight line no matter the points used.