how do know if an equation is linear or not

Answer 1

An equation that forms a straight line graph and the standard form of the linear equation is Ax+By=C.

Examples:

1. x  =  6  

This is linear equation, since this in the form of standard equation Ax + 0y = C.

1. x + 3y = 6

This is linear equation, since this in the form of standard equation Ax + By = C.

1. x + 1/y = 6

             Rewrite the equation in standard form. Clear the fraction by multiplying with y.

             xy+ 1 = 6y. Observe the xy term degree is 2. So, it’s a nonlinear equation.

1. y = x^2 + x + 4 - nonlinear equation

             The exponent on the variable x is more than one. So, it’s a noninear equation.

By simply looking, it’s linear if: 

1. There is one and only one variable that it asks you to solve for.
2. All variables appear in the numerator. (In other words, no variable should appear in the denominator if there is a fraction).
3. No variable appears inside a radical (Iinside a square root, cube root, etc.)
4. The variable must be "to the 1^st" power. (The variable must not be raised to a power.
5. There are no trigonometric functions in it.

I hope it helps a lil.

Answer 2

√2x+ 3y = 6 is nonlinear equation.