how do i know this equation is linear

kpi94 said:
2x-1 /4

2x minus 1 divided by 4
Click to expand...

As you have typed them, both expressions above represent this: \(\displaystyle 2x \;-\; \frac{1}{4}\)

Use grouping symbols to denote \(\displaystyle \frac{2x - 1}{4}\)

Like this: 2y = (2x-1)/4

We can "see" that this equation is linear by inspection (i.e., both variables are raised to the power of 1) and​ there are no operations that would change this fact.

We can also determine that this equation is linear by solving for y and realizing that the resulting equation is of the form

y = mx + b


Remember that \(\displaystyle \frac{2x - 1}{4}\) is the same as \(\displaystyle \frac{1}{4} (2x - 1)\) and that simplifies to \(\displaystyle \frac{1}{2}x - \frac{1}{4}\)

If I wrote anything that you do not understand, please ask specific questions. Cheers ~ Mark:cool:
 
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