# Question #eea8c

May 11, 2017

Choose $x$ values (even numbers in this case) and work out a $y$ value for each.
Draw a set of $x - y$ axes and mark where the points are.

#### Explanation:

OK, let's take this step by step ....

1. You have an equation. (because there is an equal sign.)
It needs to be solved, which means find values for the variables $x \mathmr{and} y$ which will make it true.

2. There is a problem! If it had ONE variable, like just $x$, it would be easy... If $3 x + 4 = 25$, we can work out that $x = 7$

BUT, there are TWO variables .....this means there are many, many values for $x$ and $y$ which will make this true.

$3 \text{ }$ Find some values which work .... this means choose an $\textcolor{red}{x}$-value and work out a $\textcolor{b l u e}{y}$ from the equation.

It will help to choose EVEN values of $x$, because we need to divide $x$ by 2 and then multiply by $- 3$ and add $12$."

If $\textcolor{red}{x = 6}$ .... what is $\textcolor{b l u e}{y}$?

$y = - \frac{3}{2} \left(\textcolor{red}{6}\right) + 12 \text{ "rarr" } y = \textcolor{b l u e}{+ 3}$

If $\textcolor{red}{x = 10}$ .... what is $\textcolor{b l u e}{y}$?
$y = - \frac{3}{2} \left(\textcolor{red}{10}\right) + 12 \text{ "rarr" } y = \textcolor{b l u e}{- 3}$

If $\textcolor{red}{x = 0}$ .... what is $\textcolor{b l u e}{y}$?
$y = - \frac{3}{2} \left(\textcolor{red}{0}\right) + 12 \text{ "rarr" } y = \textcolor{b l u e}{12}$

If $\textcolor{red}{x = - 8}$ .... what is $\textcolor{b l u e}{y}$?
$y = - \frac{3}{2} \left(\textcolor{red}{- 8}\right) + 12 \text{ "rarr" } y = \textcolor{b l u e}{24}$

$4 \text{ }$ So you can see that for ANY value you choose for $\textcolor{red}{x}$ , you can find a matching $\textcolor{b l u e}{y}$ answer.

So far we have the following pairs of values: $\left(\textcolor{red}{x , \textcolor{b l u e}{y}}\right)$
$\left(\textcolor{red}{6} , \textcolor{b l u e}{3}\right)$, $\left(\textcolor{red}{10} , \textcolor{b l u e}{- 3}\right)$, $\left(\textcolor{red}{0} , \textcolor{b l u e}{12}\right)$,$\left(\textcolor{red}{- 8} , \textcolor{b l u e}{24}\right)$
You could do this over and over and over..

This step is often done in the form of a table.

$5 \text{ }$ Plot points means: now that you have worked out matching pairs of $\left(x , y\right)$ values, draw up a set of axes and plot the points on the grid.

The $x$ is the first number and the $y$ is the second.

If you plot (draw/mark) the points we have shown above, they will all lie in a straight line and you can draw a line (graph) through them. graph{y = -3/2x+12 [-15.42, 24.58, -5.36, 14.64]}