Direct and Inverse Proportion – Review Flashcards

Twelve question-and-answer flashcards covering definitions, graphical characteristics, calculations, and examples of direct and inverse proportion.

What is meant by direct proportion between two variables?

Two variables are in direct proportion when changing one changes the other by the same scale factor; the relationship is written y ∝ x or y = kx.

What does the graph of a directly proportional relationship look like?

A straight line through the origin (0, 0) whose gradient equals the constant of proportionality k.

Give a real-life example of direct proportion.

The circumference C of a circle is directly proportional to its radius r: C = 2πr.

How do you calculate the constant of proportionality in a direct proportion?

Rearrange y = kx to k = y ⁄ x, then substitute any known pair (x, y).

What is meant by inverse proportion between two variables?

Two variables are in inverse proportion when changing one changes the other by the reciprocal of the scale factor; the relationship is y ∝ 1⁄x or y = k⁄x.

What does the graph of an inverse proportion look like?

A hyperbolic curve with asymptotes at x = 0 and y = 0; the curve approaches but never touches these axes.

How do you find the constant of proportionality in an inverse proportion?

Use y = k ⁄ x, substitute known x and y values, then solve for k.

If a container has volume 12 m³ and gas pressure 0.125 N/m² (P = k ⁄ V), what is k?

k = P × V = 0.125 × 12 = 1.5.

If m is directly proportional to n and m = 12 when n = 3, what is the constant of proportionality?

k = m ⁄ n = 12 ⁄ 3 = 4.

If p is inversely proportional to q and p = 3 when q = 5, what is the constant of proportionality?

k = p × q = 3 × 5 = 15.

What type of curve does y = k ⁄ x produce, and what are its asymptotes?

It produces a hyperbola with asymptotes at x = 0 and y = 0.

Why might an inverse-proportion model include a restriction such as t > 1?

Real-world constraints (e.g., time cannot be zero or negative) can limit the domain over which the model is valid.