# Is 0.3x+y=2 a linear function?

Nov 7, 2016

Yes; any relation that can be expressed in the form
$\textcolor{w h i t e}{\text{XXX}} y = \textcolor{red}{m} x + \textcolor{b l u e}{b}$
can be considered to be a linear function.

#### Explanation:

$0.3 x + y = 2$
$\textcolor{w h i t e}{\text{XXX")hArr y=color(red)(} \left(- 0.3\right)} x + \textcolor{b l u e}{2}$

Nov 7, 2016

This equation meets all the criteria and is the equation of a straight line.

#### Explanation:

The word 'linear' means 'in a straight line'

The equation of a straight line has the general form

$a x + b y + c = 0 \text{ } \leftarrow$ an x-term, a y-term and a number term

• the variables do not have powers more than 1,
• variables do not occur in the denominator of a fraction.
• different variables do not appear in the same term

$0.3 x + y = 2$ has an x-term, a y-term and a number term.

It can be written as:

$0.3 x + y - 2 = 0 \text{ } \leftarrow$ this is the general form of a straight line.

y = -0.3x+2" larr this is the form $y = m x + c$

$0.3 x + y = 2 \text{ } \leftarrow$ this is in standard form of a straight line.

This equation meets all the criteria and is the equation of a straight line.