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03. Coordinate Planes and Graphs

Dated: 30-10-2024

Plane

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\(b\) is called the y-coordinate or ordinate and \(a\) is called the x-coordinate or abscissa.

Quadrants

The plane can be divided into 4 quadrants.
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Graphs

The order pairs which satisfy any equation consisting of variables \(x\) and \(y\), make a graph collectively.
Here's an example

Intercepts

These are the points where graph intersect the axes of the coordinate plane.

A graph is made from 2 quantities or variables. So to find the intercept with respect to one variable, we assume the other one to be \(0\).

Example

\[3x + 2y = 6\]

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\(x\) Intercept

\[3x + 2(0) = 6\]
\[x = \frac{6}{3} = 2\]

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\(y\) Intercept

\[3(0) + 2y = 6\]
\[2y = 6\]
\[y = \frac{6}{2} = 3\]

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Symmetricity

The axes themselves act like a mirror.
The numbers \((a, b)\) and \((-a, b)\) are symmetric about y-axis.
Similarly, the numbers \((a, b)\) and \((a, -b)\) are symmetric about x-axis.
This simplifies the sketching of graphs.

Example

\[x = |y|\]

This yields 2 possibilities. \(x = y\) and \(x = -y\).
Notice how absolute value1 of \(y\) never changes, hence the graph is symmetric about x-axis
Now if we plot one of them, say \(x = y\)
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Similarly, for the \(x = -y\), we can just reflect it.
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References

Read more about notations and symbols.

  1. Read more about absolute values. ↩