Question

State whether each equation or function is linear. Write yes or no. If no, explain your reasoning.

$x+\sqrt{y}=4$

Short answer

No, the equation $x+\sqrt{y}=4$ is not a linear equation.

Step-by-step solution

– Definition of a linear equation and linear function.

In a linear equation the exponent of each variable is 1 and the variables may not be multiplied together. The graph of a linear equation is always a line.

In a linear function, each input value has a unique output value. In other words, for each point in domain, there is a unique value in the range of function. It can be written as $f\left(x\right)=mx+b$, where m and b are real numbers.

– Given information.

The given equation is:

$x+\sqrt{y}=4$

The given equation can be rewritten as:

$x+y^{\frac{1}{2}}=4$

– Check whether the equation is linear or not.

In the equation $x+y^{\frac{1}{2}}=4$, the exponent of variable x is 1 and the exponent of variable y is $\frac{1}{2}$. So, the equation $x+y^{\frac{1}{2}}=4$ is not a linear equation.

The equations $x+\sqrt{y}=4$ and $x+y^{\frac{1}{2}}=4$ are equivalent. So, the equation $x+\sqrt{y}=4$ is not a linear equation.

Thus,the required answer is “No” because the equation $x+\sqrt{y}=4$ is not a linear equation.