Question

a) Describe how you know that a graph is proportional.

b) Describe how you know an equation is proportional. Give an example of an equation that is proportional and a graph that is not proportional.

c) Describe how you know that a table is proportional

Answer 1

[AI-generated answer — Bot GPT 3.5]

a) A graph is proportional when the relationship between the variables represented on the graph is a straight line that passes through the origin (0, 0). This means that as one variable increases, the other also increases at a constant rate.

b) An equation is proportional when it can be written in the form y = kx, where k is a constant. This means that the dependent variable y is directly proportional to the independent variable x.

For example, the equation y = 2x is proportional. As x increases, y also increases at a constant rate, which is 2 in this case. On the other hand, the equation y = x^2 is not proportional because the dependent variable y increases at an increasing rate as x increases.

Here is an example of a graph that is not proportional:
- A graph that represents the relationship between time and distance for a car accelerating from rest. Initially, the car covers smaller distances in a shorter amount of time, but as it accelerates, the distances covered increase at an increasing rate.

c) A table is proportional when the ratio of the values in the second column to the corresponding values in the first column is constant. Each value in the second column is obtained by multiplying the value in the first column by the same constant.

For example, consider the following table:

x | y
-----------
1 | 2
2 | 4
3 | 6

The table is proportional because the ratio of y to x is always 2, with each value in the second column obtained by multiplying the value in the first column by 2.