Linear Relationships and Functions

The video tutorial covers various mathematical problems, including profit calculation from t-shirt sales, population growth over time, distance remaining in a travel scenario, matching functions to graphs, identifying linear relationships, and understanding rate of change in a pizza buffet context. Each section provides step-by-step guidance on solving these problems using equations, graphs, and logical reasoning.

What is the formula for calculating profit when selling multiple t-shirts?

• Profit = (Selling Price - Cost Price) * Number of T-Shirts

• Profit = Selling Price * Number of T-Shirts

• Profit = Cost Price * Number of T-Shirts

• Profit = Selling Price - Cost Price

If a t-shirt sells for $17.56 and costs $12.01 to produce, what is the profit per t-shirt?

• $4.55

• $5.55

• $5.00

• $6.55

In what year will the population of a town be 16,736 if it grows from 1940?

• 1979

• 1980

• 1978

• 1981

How many miles will Alex have left after traveling for 7 hours if he starts with 2075 miles?

• 717 miles

• 911 miles

• 1105 miles

• 500 miles

What is the rate of change in miles per hour for Alex's flight?

• 194 miles per hour

• 200 miles per hour

• 190 miles per hour

• 180 miles per hour

Which of the following equations matches a graph with a y-intercept of -1/2 and a slope of 2/3?

• y = 2/3x + 1/2

• y = 3/2x - 1/2

• y = 2/3x - 1/2

• y = 3/2x + 1/2

Which table corresponds to a graph where x = 0 results in y = 0?

• Table D

• Table A

• Table B

• Table C

Which scenario represents a linear relationship?

• The cost of living increases by 3% each year.

• A radioactive substance loses half its mass every 12 years.

• The volume of a cube depends on its side length.

• Someone loses 5 pounds every month.

What does the slope represent in the equation y = 14x + 18 for pizza production?

• 18 pizzas per 18 minutes

• 14 pizzas per 18 minutes

• 18 pizzas per 9 minutes

• 14 pizzas per 9 minutes

If 14 pizzas are placed every 9 minutes, how many pizzas are placed every 18 minutes?

• 14 pizzas

• 28 pizzas

• 18 pizzas

• 24 pizzas