Question

In algebra, we often study relationships where a change to one variable causes change

Answer 1

A familiar situation describing where one quantity changes constantly in relation to another quantity is: the amount you pay as cost for buying gas at a gas station in relation to the quantity of gas you buy.

The two quantities, (cost and quantity of gas) are directly proportional.

When you represent the relationship of cost of gas and quantity of gas on a graph, you will have: a proportional graph with cost ($) on the y-axis and quantity of gas (gallons) on the x-axis.

(see attachment for how the graph will look like.)

There are usually two variables:

• Independent variable which causes the change.

• Dependent variable which responds to the change caused by the independent variable.

A situation where one quantity (dependent variable) changes constantly in relation to another quantity (independent variable) is a situation of the amount you pay at a gas station for filling your car with a certain quantity of gallons of gas.

The two quantities are directly proportional to each other.

That is:

• The cost of gas in dollars (independent variable) is directly proportional to the quantity of gas in gallons (dependent variable).

• As the quantity of gas increased in gallons, there would be equal increase in the cost of gas in dollars you would pay.

If we are to represent this on a graph, the graph will be a straight line graph showing a proportional relationship between cost of gas (on the y-axis) and quantity of gas (on the x-axis)

(see the image in the attachment below).

Therefore:

• A familiar situation describing where one quantity changes constantly in relation to another quantity is: the amount you pay as cost for buying gas at a gas station in relation to the quantity of gas you buy.

• The two quantities, (cost and quantity of gas) are directly proportional.

• When you represent the relationship of cost of gas and quantity of gas on a graph, you will have: a proportional graph with cost ($) on the y-axis and quantity of gas (gallons) on the x-axis.

(see attachment for how the graph will look like.)

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