Practice: Proportional relationships, direct and inverse variation | Pre-algebra

Work each problem out on paper before you open the solution. If your answer is off, compare the steps and find where you went wrong. If a problem stops you cold, go back to the lesson: every set links to it.

Warm-up

Practice 1

Does this table show direct variation, inverse variation, or neither? Find the constant.

$$x$$	$$3$$	$$5$$	$$8$$	$$10$$
$$y$$	$$12$$	$$20$$	$$32$$	$$40$$

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The ratio $\frac{y}{x}$ is always $$4$$ : direct variation, $$y = 4x$$ .

Level up

Practice 4

Direct variation, inverse variation, or neither?

$$x$$	$$1$$	$$2$$	$$4$$
$$y$$	$$5$$	$$8$$	$$14$$

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Ratios: $$5$$ , $$4$$ , $$3.5$$ . Not constant. Products: $$5$$ , $$16$$ , $$56$$ . Not constant either.

Neither. (The values follow $$y = 3x + 2$$ : $$y$$ grows steadily with $$x$$ , but a proportional relationship would also need $$y = 0$$ when $$x = 0$$ .)

Word problems

Quick check

Practice 8Quick check

Which pair of quantities is directly proportional?

Practice 9Quick check

$$y$$ is directly proportional to $$x$$ , and $$y = 15$$ when $$x = 5$$ . What is $$y$$ when $$x = 8$$ ?