Question

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

$y=\sqrt{2x-5}$

Short answer

No, the equation $y=\sqrt{2x-5}$ 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:

$y=\sqrt{2x-5}$

Taking square on both sides.

$\begin{array}{l}{y}^2={\left(\sqrt{2x-5}\right)}^2\\ y^2=2x-5\end{array}$

– Check whether the equation is linear or not.

In the equation $y^2=2x-5$the exponent of x is 1 and the exponent of y is 2.

The equation $y^2=2x-5$is not a linear equation because y has an exponent other than 1.

The equation $y^2=2x-5$is equivalent to $y=\sqrt{2x-5}$. So, the equation $y=\sqrt{2x-5}$is not linear.

Thus,the required answer is “No” because the equation $y=\sqrt{2x-5}$is not a linear equation.