Direct Proportion Flashcards

All 5 cards in this deck

What equation do you write when $y$ is directly proportional to $x$?

$y = kx$, where $k$ is the constant of proportionality.

What are the steps to answer a question on proportion to a root?

e.g. $y \propto \sqrt{x}$, $y = 10$ when $x = 4$; find $y$ when $x = 25$

1. Write the equation: $y = k\sqrt{x}$
2. Substitute the known pair to find $k$: $10 = k \times 2$, so $k = 5$
3. Substitute the new value: $y = 5 \times 5 = 25$

On a graph of $y$ against $x$ showing direct proportion, what shape is the graph and what does its gradient give?

A straight line through the origin; the gradient is the constant of proportionality $k$.
e.g. a line through $(4,5)$ gives $k = 1.25$.

True or false? If $y$ goes up by the same amount every time $x$ goes up by 2, then $y$ must be directly proportional to $x$.

False. $y \div x$ must be the same for every pair (equivalently, the graph must pass through the origin).

What are the steps of the unitary method for a direct proportion problem?

e.g. 4 identical boxes of seed cover $60$ m$^2$; what area do 7 boxes cover?

1. Divide to find the amount for one: $60 \div 4 = 15$ m$^2$ per box
2. Multiply by the number wanted: $15 \times 7 = 105$ m$^2$