You are hosting a party at a restaurant. The restaurant charges $150 to reserve the room plus $25 per person for food and drink.


1. Write a linear equation representing your total bill based on the number of people at your party.

2. If you graph this line, what is its slope?

3. What does the slope represent in this scenario?

A standard linear equation is

y=mx+b,

y=cost in this case
x=number of people
m=slope, and represents unit increase in y (cost in this case) per unit increase in x (number of people)
b=fixed cost, i.e. cost even when nobody shows up.

Post your answers if you need confirmation.

1. C=25P+150. C=Total cost. P=The number of people attending.

2. Slope=25

3. The slope represents the cost per person.

1. To write a linear equation representing the total bill based on the number of people at your party, we need to consider the fixed cost of reserving the room ($150) and the variable cost per person for food and drink ($25). Let's call the total bill B and the number of people at the party P. The equation can be written as:

B = 150 + 25P

2. To find the slope of the graph of this linear equation, we need to rearrange the equation in slope-intercept form (y = mx + b). In this case, the equation is already in that form, with B as the dependent variable (y) and P as the independent variable (x). Therefore, the slope (m) is the coefficient of P, which is 25.

3. In this scenario, the slope represents the additional cost per person for food and drink. It tells us that for each additional person attending the party, the total bill increases by $25. So, if you have 10 more people attending the party, the total bill would increase by 10 * $25 = $250. The slope provides information about the rate of change in the total bill as the number of people increases.