We are given the equation:

$x + 5y = 13$

Part (a): Solve for $y$ in terms of $x$

1. Isolate $y$:

   $5y = 13 - x$

2. Divide both sides by 5:

   $y = \frac{13 - x}{5}$

Now, replace $y$ with function notation $f(x)$:

$f(x) = \frac{13 - x}{5}$

Part (b): Find $f(12)$

Substituting $x = 12$ into $f(x)$:

$f(12) = \frac{13 - 12}{5} = \frac{1}{5}$

Thus,

$f(12) = \frac{1}{5}$

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Related Questions:

1. What is the domain and range of $f(x)$?
2. How do you find the x- and y-intercepts of $f(x)$?
3. What is the slope of the function $f(x)$ and what does it represent?
4. How do you determine if a function is linear?
5. How do you evaluate $f(a)$ for any given number $a$?

Tip:

For any linear equation in the form $ax + by = c$, solving for $y$ in terms of $x$ gives the slope-intercept form $y = mx + b$, which helps to easily identify the slope and y-intercept.