To reflect a function $f(x)$ across the y-axis, we replace $x$ with $-x$ in the function. This means that the function $g(x)$, which is the reflection of $f(x)$, is given by:

$g(x) = f(-x)$

The given function is:

$f(x) = -x + 6$

Now, we replace $x$ with $-x$ in $f(x)$ to find $g(x)$:

$g(x) = -(-x) + 6 = x + 6$

So the reflection of $f(x) = -x + 6$ across the y-axis is:

$g(x) = x + 6$

This is already in the form $mx + b$, where $m = 1$ and $b = 6$.

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Do you need any further clarification on this process? Or perhaps you'd like more examples?

Here are 5 related questions for you to explore:

1. How would you reflect a quadratic function, such as $f(x) = x^2 + 3x - 2$, across the y-axis?
2. How would you find the reflection of $f(x) = 3x - 5$ across the x-axis instead of the y-axis?
3. If $g(x) = x + 6$, what would $g(x)$ look like after reflecting across the x-axis?
4. How can you describe the general form of any linear function's reflection across the y-axis?
5. How does reflecting a function across the y-axis affect its slope and intercept?

Tip: Remember, reflecting a function across the y-axis only changes the sign of $x$ inside the function.