**y = mx + c**,

wheremis the gradient andcis the intercept on the vertical axis (y).

When a straight line is plotted, we get a simple straight line cutting across the y axis at the point indicated by the constant "c" in the general straight line equation.

Diagram 1: A straight line graph y = 2x + 1 with x-axis as "x".

What if the equation is y = 2x

^{2}+ 1 ?

Is it still a straight line when the horizontal axis is "x"? Let us see the diagram below.

Diagram 2: y = 2x

^{2}+ 1 is

**not a straight line**when the horizontal axis is "x".

Now, let us replace the "x

^{2}" in the expression with "z" and see what happens to the graph when plotted with the horizontal axis as "z".

Diagram 3: A straight line graph with horizontal axis plotted as "z".

From diagram 3, we can see that by replacing the original "x

^{2}" with "z", we can

**convert**the parabolic curve of diagram 2 to

**a straight line graph**.

This is so because the equation y = 2

**x**+ 1 is now expressed as y = 2

^{2}**z**+ 1 , a straight line general format!

In other words, when we plot y = 2x

^{2}+ 1 in the graph format "y against x

^{2}", we should expect a straight line graph.

Let's do another example:

y = 2/x + 3

Plotting this against horizontal axis of "x" gives the below graph.

Diagram 4: Graph when plotted with horizontal axis as "x".

Now, when we substitute the horizontal axis with (1/x), we should be getting a straight line graph following the principle we applied in the previous example.

Diagram 5: Straight line graph with horizontal axis plotted as "1/x".

When we are able to convert any mathematical expression to the straight line format

y = mx + c, and apply the horizontal scale according, we can reduce the complexity of graphical curve to a simple straight line, which will be easy enough for analysis.

When concepts and principle of mathematical operations are understood, a complex problem can be reduced to a simple question as with the graphical technique of above. After all, a straight line is still much easier to handle than a curve with varying gradient.

:)

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