Question

1. Each pair of values below represents the values of two proportional variables. Give an equation for y in terms of x. (a) x=4 and y = 28 (b) x = 48 and y = 24 (C) x=14 and y=21

Answer 1

To write an equation in which y and x are proportional variables there must be an equation with a constant of proportionality like this:

$y=kx$

using the values of y and x find the value of the constant of proportionality.

a)

$\begin{gathered} 28=k\cdot4 \\ k=\frac{28}{4} \\ k=7 \end{gathered}$

the equation is

$y=7x$

b)

$\begin{gathered} 24=k\cdot48 \\ k=\frac{24}{48} \\ k=\frac{1}{2} \end{gathered}$

the equation is

$y=\frac{1}{2}x$

c)

$\begin{gathered} 21=k\cdot14 \\ k=\frac{21}{14} \\ k=\frac{3}{2} \end{gathered}$

the equation is

$y=\frac{3}{2}x$