Direct and inverse proportion

Direct and inverse proportion

Direct Proportion

If you divide any two related variables, and you always get the same result, then those variables are said to be in direct proportion. The result from the division, quotient, is the constant of proportionality.

Multiple Choice

If variables x and y are in direct proportion and k is a constant, then a valid equation for these variables is

• y + x = k

• y - x = k

• xy = k

• $\frac{y}{x}=k$

Inverse proportion

If you multiply any two related variables, and you always get the same product, then those variables are said to be in inverse proportion. The result from the division, product, is the constant of proportionality..

Multiple Choice

If variables x and y are in inverse proportion and k is a constant, then a valid equation for these variables is

• y + x = k

• y - x = k

• xy = k

• $\frac{y}{x}=k$

Multiple Choice

If variables x and y are in direct proportion, then a possible table for these variables is

Multiple Choice

If variables x and y are in inverse proportion, then a possible table for these variables is

Multiple Select

In a direct proportion if one variable increases, so does the other one. This table, though it satisfies this condition, does not represent a direct proportion. Why is that so?

• It does not include (0,0)

• The product of the variables is not constant

• The quotient of the variables is not constant

• Because I say so

Multiple Select

Which of the following situations may be modeled as a direct proportion? Select all that apply.

• To prepare a loaf of banana bread a recipe says you need to put 1 tablespoon to the dough for each 2 bananas you use.

• To drive from Santiago to Antofagasta you need to cover 1335 km in the Ruta 5. The average speed (v) at which you drive in this stretch and the time (t) you take to arrive at Antofagasta

• The total cost C for Q units of a certain product at a fixed unit price

• The unit price P and the total cost C of a fixed number of units of a certain product

Multiple Select

Which of the following situations may be modeled as an inverse proportion? Select all that apply.

• To prepare a loaf of banana bread a recipe says you need to put 1 tablespoon to the dough for each 2 bananas you use.

• To drive from Santiago to Antofagasta you need to cover 1335 km in the Ruta 5. The average speed (v) at which you drive in this stretch v the time (t) you take to arrive at Antofagasta.

• The total cost C for Q units of a certain product at a fixed unit price

• The unit price P and the total cost C of a fixed number of units of a certain product

Multiple Select

Which of the following situations may be modeled as a direct proportion? Select all that apply.

• To prepare a loaf of banana bread a recipe says you need to put 1 tablespoon to the dough for each 2 bananas you use.

• To drive from Santiago to Antofagasta you need to cover 1335 km in the Ruta 5. The average speed (v) at which you drive in this stretch and the time (t) you take to arrive at Antofagasta

• The total cost C for Q units of a certain product at a fixed unit price

• The unit price P and the total cost C of a fixed number of units of a certain product

Graph of a direct and inverse proportion

The graph for two variables in direct proportion is always is always a straight line starting and including the origin.

The graph for two variables in inverse proportion is always is always a curve approaching both axes.

Multiple Choice

If variables x and y are in direct proportion and k is a constant, then a possible graph for these variables is

Multiple Choice

To drive from Santiago to Antofagasta you need to cover 1335 km in the Ruta 5. If your average speed is 92 km/h you will take 14 hours an a half to arrive at Antofagasta. If we consider this situation as a proportionality, then the value of its constant of proportionality is

• 1335 km

• 92 km/h

• 14.5 hours

• 5

Multiple Choice

If variables x and y are in inverse proportion and k is a constant, then a possible graph for these variables is