State whether each equation or function is linear. Write yes or no. If no, explain your reasoning.
No, the equation is not a linear equation.
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 , where m and b are real numbers.
The given equation is:
Taking square on both sides.
In the equation the exponent of x is 1 and the exponent of y is 2.
The equation is not a linear equation because y has an exponent other than 1.
The equation is equivalent to . So, the equation is not linear.
Thus, the required answer is “No” because the equation is not a linear equation.
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