Question #eea8c

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 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 `3x +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" "` Find some values which work .... this means choose an `color(red)(x)`-value and work out a `color(blue)(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 `color(red)(x=6)` .... what is `color(blue)(y)`?

`y = -3/2 (color(red)(6))+12" "rarr" " y = color(blue)(+3)`

If `color(red)(x=10)` .... what is `color(blue)(y)`?
`y = -3/2 (color(red)(10))+12" "rarr" " y = color(blue)(-3)`

If `color(red)(x=0)` .... what is `color(blue)(y)`?
`y = -3/2 (color(red)(0))+12" "rarr" " y = color(blue)(12)`

If `color(red)(x=-8)` .... what is `color(blue)(y)`?
`y = -3/2 (color(red)(-8))+12" "rarr" " y = color(blue)(24)`

`4" "` So you can see that for ANY value you choose for `color(red)(x)` , you can find a matching `color(blue)(y)` answer.

So far we have the following pairs of values: `(color(red)(x,color(blue)(y)))`
`(color(red)(6),color(blue)(3))`, `(color(red)(10),color(blue)(-3))`, `(color(red)(0),color(blue)(12))`,`(color(red)(-8),color(blue)(24))`
You could do this over and over and over..

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

`5" "` Plot points means: now that you have worked out matching pairs of `(x,y)` 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]}