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secondary 3 | A Maths
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Its linear law qn . How to do?
Y = mX + c
y = m (y/x) + c
[We always plot VERTICAL against HORIZONTAL, so if they say things like plot x against y, then x is on the vertical axis and y is on the horizontal axis]
With gradient 2 and vertical intercept -1 (here the vertical axis is y and the horizontal axis is y/x),
y = 2 (y/x) - 1
Now we rearrange our variables to make y alone as per the given equation.
Multiplying both sides by x,
xy = 2y - x
xy - 2y = -x
y (x - 2) = -x
y = -x / (x - 2)
where a = -1 and b = 2.
Simul by substitution is perfectly acceptable though.
The method I was talking about, in the spirit of this chapter (though almost every student would just do simul instead).
If y = 3x, then y/x = 3
Substituting this into the equation y = 2 (y/x) - 1,
y = 2 (3) - 1
y = 5
[Graphically, this represents X = 3 (i.e. y/x = 3); we trace this on the graph to find the corresponding Y-coordinate; we will get Y = 5 (i.e. y = 5)]
Since y = 5,
y/x = 3
5/x = 3
x = 5/3
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