OK, let's take this step by step ....
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You have an equation. (because there is an equal sign.)
It needs to be solved, which means find values for the variables x and yxandy which will make it true.
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There is a problem! If it had ONE variable, like just xx, it would be easy... If 3x +4 =253x+4=25, we can work out that x =7x=7
BUT, there are TWO variables .....this means there are many, many values for xx and yy which will make this true.
3" "3 Find some values which work .... this means choose an color(red)(x)x-value and work out a color(blue)(y)y from the equation.
It will help to choose EVEN values of xx, because we need to divide xx by 2 and then multiply by -3−3 and add 1212."
If color(red)(x=6)x=6 .... what is color(blue)(y)y?
y = -3/2 (color(red)(6))+12" "rarr" " y = color(blue)(+3)y=−32(6)+12 → y=+3
If color(red)(x=10)x=10 .... what is color(blue)(y)y?
y = -3/2 (color(red)(10))+12" "rarr" " y = color(blue)(-3)y=−32(10)+12 → y=−3
If color(red)(x=0)x=0 .... what is color(blue)(y)y?
y = -3/2 (color(red)(0))+12" "rarr" " y = color(blue)(12)y=−32(0)+12 → y=12
If color(red)(x=-8)x=−8 .... what is color(blue)(y)y?
y = -3/2 (color(red)(-8))+12" "rarr" " y = color(blue)(24)y=−32(−8)+12 → y=24
4" "4 So you can see that for ANY value you choose for color(red)(x)x , you can find a matching color(blue)(y)y answer.
So far we have the following pairs of values: (color(red)(x,color(blue)(y)))(x,y)
(color(red)(6),color(blue)(3))(6,3), (color(red)(10),color(blue)(-3))(10,−3), (color(red)(0),color(blue)(12))(0,12),(color(red)(-8),color(blue)(24))(−8,24)
You could do this over and over and over..
This step is often done in the form of a table.
5" "5 Plot points means: now that you have worked out matching pairs of (x,y)(x,y) values, draw up a set of axes and plot the points on the grid.
The xx is the first number and the yy 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]}
