Question #eea8c

1 Answer
May 11, 2017

Answer:

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 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]}