# Is y=x^2+3 a linear function?

Nov 6, 2016

There is a term in ${x}^{2}$ so the function is not linear.
It is a parabola.

#### Explanation:

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

The equation of a straight line has the general form

$a x + b y + c \text{ } \leftarrow$ 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

In this case, there is a term in ${x}^{2}$ so the function is not linear.
It is a parabola.