https://file.aiquickdraw.com/mathbot/file/1728527967846ktrooop5.jpg

In this problem, we are dealing with a linear equation that models the cost of a birthday party at a pottery studio. Here's the breakdown:

### Part A:
The studio charges a set fee for birthday parties plus $12.95 for each person. Annalise's birthday party for 8 people cost $198.60. The equation given in point-slope form is:

\[
y - 198.60 = 12.95(x - 8)
\]

This equation represents the total cost of the party (denoted by $y$) based on the number of people at the party (denoted by $x$), with $198.60 being the total cost for 8 people and $12.95 the cost per person.

### Part B:
The next question asks for the y-intercept, which is the fixed cost of the party without including any additional people. In this case, the y-intercept is 95, meaning the studio charges a base fee of $95 for hosting the party, and the rest is the cost for the people attending.

Do you need further clarification or details on this? Here are some related questions for deeper understanding:

1. How do you convert from point-slope form to slope-intercept form?
2. How would the equation change if the cost per person increased?
3. What does the slope of the equation represent in this context?
4. How can you determine the total cost for a different number of people using this equation?
5. What if there is a discount for groups larger than 10—how would that affect the equation?

**Tip**: In word problems, always identify what variables represent (e.g., $x$ is the number of people, and $y$ is the total cost) to translate real-world situations into equations more easily.

A pottery studio charges a set fee for birthday parties plus $12.95 for each person at the party. Annalise's birthday party for 8 people cost $198.60.

Learn how to write a linear equation in point-slope form for a pottery studio's birthday party charges, which include a set fee and an additional cost per person. The total cost for 8 people is $198.60, with each person costing $12.95. This is suitable for students in Grades 7-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation