Question

If y varies directly as x, then find the values of a and b from the following table:

x	8	6	10	b
y	12	a	15	21

Answer 1

y varies directly as x

$\Rightarrow y\infty x$

$\Rightarrow y=kx$ where k is some constants

when $x=8$, y is $12$

$12=k\left(8\right)$

$\Rightarrow k=\frac{3}{2}$

when $x=6$, y is a

$\Rightarrow a=k\left(6\right)$

$a=\frac{3}{2}\left(6\right)$

$\Rightarrow a=9$

when $x=b$, y is $21$

$\Rightarrow 21=k\left(b\right)$

$21=\frac{3}{2}\left(b\right)$

$\Rightarrow b=14$.