Determine whether the equation defines y as a linear function of x. If so, write it in the form y = mx + b. (If an answer does not exist, enter DNE.)
2x2 − 8y + 6 = 0
Yes
No    

y = 
 

To determine if the equation defines \( y \) as a linear function of \( x \), we need to analyze the equation step by step.

The given equation is:

\[
2x^2 - 8y + 6 = 0
\]

### Step 1: Solve for \( y \)
Let's try to isolate \( y \):

\[
-8y = -2x^2 - 6
\]

Now, divide both sides by \(-8\):

\[
y = \frac{2x^2 + 6}{8}
\]

Simplify the fraction:

\[
y = \frac{x^2}{4} + \frac{3}{4}
\]

### Step 2: Analyze the form
The equation is now \( y = \frac{x^2}{4} + \frac{3}{4} \). Since \( x^2 \) appears in the equation, this is a **quadratic function**, not a linear function. A linear function has the form \( y = mx + b \), where the highest degree of \( x \) is 1, but here we have \( x^2 \), which makes it non-linear.

Thus, the equation does **not** define \( y \) as a linear function of \( x \).

The correct answer is **No**.

Let me know if you have any questions, or if you need further details!

### Additional Questions:
1. What defines a linear function in terms of degree?
2. How do quadratic functions differ from linear functions?
3. Can you give an example of a linear equation with different coefficients?
4. How can you transform a quadratic equation into its standard form?
5. What is the significance of the \( x^2 \) term in the equation?

### Tip:
Always check the degree of the variables in the equation to quickly determine if it is linear, quadratic, or another type of function.

Determine whether the equation defines y as a linear function of x. If so, write it in the form y = mx + b. (If an answer does not exist, enter DNE.) 2x^2 − 8y + 6 = 0

Explore whether the equation 2x^2 − 8y + 6 = 0 defines y as a linear function of x. Understand how to identify linear vs. quadratic functions, and follow a detailed step-by-step solution. Suitable for students in Grades 8-10.

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