To solve the equation:

\[
-13y - 19 = 17x
\]

We need to isolate one of the variables (either \( y \) or \( x \)).

### Solving for \( y \):

1. Add 19 to both sides of the equation:
   \[
   -13y = 17x + 19
   \]

2. Divide both sides by -13 to isolate \( y \):
   \[
   y = \frac{17x + 19}{-13}
   \]
   or
   \[
   y = -\frac{17x}{13} - \frac{19}{13}
   \]

This is the expression for \( y \) in terms of \( x \).

Would you like me to explain any part in more detail or solve this for a specific value of \( x \)?

Here are five related questions for practice:
1. What is the solution for \( x \) in terms of \( y \) from the original equation?
2. How would you graph the equation \( y = -\frac{17x}{13} - \frac{19}{13} \)?
3. If \( x = 0 \), what is the value of \( y \)?
4. If \( y = 0 \), what is the value of \( x \)?
5. How would the equation change if the coefficient of \( y \) was positive?

**Tip**: Always simplify fractions when possible to make equations easier to work with!

Explore how to solve the linear equation –13y − 19 = 17x and learn to isolate variables. This step-by-step solution introduces key algebraic concepts and provides practice questions. Ideal for students in Grades 8-10.

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