How linear functions, linear equations and linear inequalities are related.

Question

Delorenzoz · Accepted Answer

All linear equations can be represented in the form

y = m x + b

. Depending upon the values of m and b, linear equations can be vertical, horizontal as well as slant.
Example of vertical linear equation is

x = 3

. Example of horizontal linear equation is

y = 2

. Example of slant linear equation is

y = - 2 x + 5

.
All linear equations which are not vertical are also called linear functions. The reason why vertical lines are excluded from the set of linear equations to get the linear functions is because all the functions must pass the vertical line test. Examples of linear functions are

y = 2 and y = - 2 x + 5

.
Linear inequalities can be obtained by replacing the equal to sign in a linear equation by an inequality sign. Examples of linear inequalities are

4 x - 7 > 5

and

- 3 x + 10 \leq 9

.
Conclusion:
Linear functions are those linear equations which are not vertical. This sums up that all linear functions are linear equations but not all linear equations are linear functions. If the equal to sign is replaced by inequality symbol then linear equation becomes linear inequality.

How linear functions, linear equations and linear inequalities are related.

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