Q4. - Algebra 2

Question

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

 

$4.x^2+y^2=4$

Step-by-Step Solution

Answer

No, the equation $x^2+y^2=4$ is not a linear equation.

Step 1 – 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.

Step 2 – Given information.

The given equation is:

 $x^2+y^2=4$

Step 3 – Check whether the equation is linear or not.

In the given equation the exponent of $v$ is $2$ and the exponent of $y$ is $2$.

The equation $x^2+y^2=4$ is not a linear equation because both $v$ and $y$ has an exponent other than $1$.

Thus, the required answer is “No” because the equation $x^2+y^2=4$ is not a linear equation