The variable $x$ is directly proportional to the variable $t$. When $t=4.6, x=3.45$. Find the value of the constant of proportionality in decimal.

The variable $x$ is directly proportional to the variable $t$. When $t=4.6, x=3.45$. Write down the function relating $t$ and $x$.

The variable $x$ is directly proportional to the variable $t$. When $t=4.6, x=3.45$. Find $x$ when $t=8.2$

$P$ is inversely proportional to $y$. When $P=15,y=0.2$. Find $P$ when $y=1.5$.

$M$ varies directly as the square of $c$. When $M=12.6, c=3$. When $M=17.15$, find $c$, where $c>0$.

$p$ is inversely proportional to the square of $q$. Find the missing values in this table:

$\begin{array}{|cccc|}\hline p& 100& & 1\\ q& & 0.4& 2\\ \hline\end{array}$

Write down the function connecting $x$ and $y$ for the given table of values:

$\begin{array}{|ccccc|}\hline x& -1& 3& 5& 8\\ y& 0.25& 2.25& 6.25& 16\\ \hline\end{array}$

Write down the function connecting $x$ and $y$ for the given table of values:

$\begin{array}{|ccccc|}\hline x& -2& -1& 0.5& 4\\ y& 2.5& 5& -10& -1.25\\ \hline\end{array}$

A supermarket sells $300\mathrm{ml}$ bottles of ketchup for $\pounds 1.30$ a bottle. Explain why total cost of ketchup is in direct proportion to the number of bottles of ketchup bought.