Linear Relationships and Functions

This video tutorial covers eighth-grade mathematics focusing on proportional and linear relationships. It explains how to understand, represent, and compare these relationships using graphs, tables, and equations. The tutorial also delves into calculating slopes, intercepts, and solving linear equations, providing practical examples and exercises to reinforce learning.

If Priya jogs 1 mile in 0.2 hours, how far does Diego bike in the same time if he is twice as fast?

• 4 miles

• 1 mile

• 2 miles

• 3 miles

In the tortoise and hare race, if the hare runs 16 miles, how many miles does the tortoise run according to the relationship y = 4x?

• 12 miles

• 8 miles

• 4 miles

• 16 miles

What is the rate of change in a linear relationship where y increases by 15 when x increases by 1?

• 10

• 15

• 25

• 20

If a customer pays $80 for pizza delivery, and the delivery fee is $3, how many pizzas did they order if each pizza costs $11?

• 8 pizzas

• 5 pizzas

• 6 pizzas

• 7 pizzas

In a painting service, if the slope of the cost line is 50, what does this represent?

• Discount on total cost

• Total cost of supplies

• Cost per gallon of paint

• Cost per hour of labor

What does the slope of a line represent in the context of a muffin delivery cost graph?

• The total cost of muffins

• The price per muffin

• The delivery charge

• The number of muffins ordered

In a recipe, if Noah uses 2 cups of sugar for every 1 cup of flour, how much flour does he need for 6 cups of sugar?

• 3 cups

• 4 cups

• 6 cups

• 2 cups

If a line has a slope of 3 and a y-intercept of 12, what is the equation of the line?

• y = 12x - 3

• y = 3x + 12

• y = 3x - 12

• y = 12x + 3

How would you describe the relationship between the number of classes attended and the total cost in a gym membership graph?

• The cost decreases with more classes

• The cost is unrelated to the number of classes

• The cost increases by a fixed amount per class

• The cost is constant regardless of classes

What is the y-intercept of the equation y = -4x + 20?

• -4

• 20

• 4

• -20