Preamble
To build a graph (2 axis style → Cartesian) we need to be able identify the values in each axis. We can assign (within limits) any value we wish to x. So it does nor matter if this is imbedded within other value/actions. We must have the y value isolated (on its own).
x is the independent variable. We can decide the value it takes.
y is the dependant variable. Its value 'depends' on the value we assign to x.
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Solving your question
Given: −x−3y=2
To isolate the terms with y in them (only 1) add x to both sides
−x+x−3y = 2+x
0−3y=2+x
Multiply both sides by -1 giving
+3y=−x−2
Divide both sides by 3
33×y=−x3−23
But 33=1
1×y=−x3−23
y=−x3−23 ...........................(1)
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You now have a choice. You can leave as is or you can factor out the 13. This option would look like:
y=13(−x−2) or even ........................(2)
y=−13(x+2).........................(3)
Equations (1) ,(2) and (3) will all plot the same curve.
To draw the graph you can build a table of values and then plot x against y
The other option is to calculate the value of x if y=0 and the value of y if x=0
![Tony B]()
![Tony B]()
