Answer:
Linear : [tex]y=22-5x[/tex]
Non linear : [tex]y=x^3\ and\ y=x^3+13[/tex]
Step-by-step explanation:
Given:
The equations given are:
[tex]y=22-5x[/tex]
[tex]y=x^3[/tex]
[tex]y=x^3+13[/tex]
Now, a linear equation is of the form:
[tex]y=mx+b[/tex]
Where, 'm' and 'b' are real numbers and 'm' not equal to 0.
The highest exponent of 'x' in a linear equation is always 'one'.
Therefore, if the exponent of 'x' in an equation is anything other than 'one', then the equation is a nonlinear equation.
The equation [tex]y=22-5x[/tex] can be rewritten as:
[tex]y=-5x+22[/tex]
The above equation is of the form of a linear equation with [tex]m=-5\ and\ b=22[/tex]. So, this represents a linear equation.
The other two equations have exponent 3 for 'x' which is not '1'. So, these equations are nonlinear equations.
