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The given equation is $ 7x - 2y = -31 $, where:

- $ x $ represents the number of movies Keisha sees, and
- $ y $ represents the total cost for $ x $ movies.

We need to answer the following questions:

**a. What was the cost of the pass?**

To find the cost of the pass, we can rewrite the equation in the form $ y = mx + b $, which will give us the fixed cost (the pass) and the cost per movie.

Starting with $ 7x - 2y = -31 $, we solve for $ y $:

\[
-2y = -7x - 31
\]

Now divide by $-2$:

\[
y = \frac{7}{2}x + \frac{31}{2}
\]

This means the total cost $ y $ consists of:
- $ \frac{7}{2}x $ or $ 3.5x $, which is the cost per movie,
- $ \frac{31}{2} $ or $ 15.5 $, which is the cost of the pass.

Thus, **the cost of the pass is \$15.50**.

**b. What is the discounted admission price for each movie?**

From the equation, $ \frac{7}{2}x $ represents the cost per movie. So, the discounted admission price per movie is **\$3.50**.

Would you like further clarification or details on this solution?

Here are 5 related questions to explore further:
1. How would the equation change if Keisha buys a different pass with a higher price?
2. What if the number of movies viewed increases to a specific value? How does this impact the total cost?
3. How can we interpret the equation if the price per movie was not discounted?
4. How would you modify the equation to reflect a scenario where the cost per movie is halved?
5. What happens if Keisha buys no movies? What does the equation imply in that case?

**Tip:** Always look to express word problems in algebraic form to simplify the solution process.

Keisha bought a discount pass at a movie theater. It entitles her to a special discounted admission price for every movie she sees. Keisha wrote an equation that gives the total cost y of seeing x movies. In standard form, the equation is 7x - 2y = -31.
a. What was the cost of the pass?
b. What is the discounted admission price for each movie?

Solve a real-life linear equation problem where Keisha buys a discount pass at a movie theater. The equation 7x - 2y = -31 is used to find both the cost of the pass and the discounted admission price for each movie. Suitable for students in Grades 7-9, this problem explores key algebraic concepts in linear equations.

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