Question

If $x$ and $y$ have a direct variation, determine the values of $a$, $b$ and $c$.

• A. $a=5$, $b=14$, $c=18$
• B. $a=9$, $b=19$, $c=11$
• C. $a=7$, $b=27$, $c=13$

Answer 1

The correct option is B $a=9$, $b=19$, $c=11$

For, direct variation:

$\frac{y}{x}=k$

From the table we have $x=6$ and $y=12$ and
Therefore, $k=\frac{12}{6}=2$

So, when $x=4.5$ , and $\frac{y}{x}=k$

$y=k\times x$

= $2\times 4.5=9$

Therefore, $a=9$

Similarly, when $x=9.5,y=2\times 9.5$
$=19$

Thus $b=19$

And, when $y=22$, and $\frac{y}{x}=k$
$x=\frac{y}{k}=\frac{22}{2}=11$

So, $c=11$

Hence, $a=9,b=19,c=11$

Option (b.) is correct.