Understanding Linear Relationships and Rates

This video tutorial covers understanding and representing proportional and linear relationships through graphs, tables, and equations. It explores concepts like slope, intercepts, and rate of change, providing examples and practice problems to enhance comprehension.

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

• 1 mile

• 2 miles

• 3 miles

• 4 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?

• 20

• 15

• 10

• 25

If a painting company charges a flat rate of $500 plus $50 per hour, how much would it cost for 20 hours of labor?

• $1000

• $1500

• $2000

• $2500

Who ran farther in 10 minutes, Tyler or Elena, if Tyler runs 1 mile in 8.33 minutes and Elena runs 1 mile in 8.5 minutes?

• Elena

• Tyler

• Not enough information

• Both ran the same distance

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

• The total cost of muffins

• The delivery charge

• The price per muffin

• The number of muffins ordered

If Noah uses 10 cups of sugar, how many cups of flour does he need according to his recipe?

• 3 cups

• 15 cups

• 10 cups

• 5 cups

How do you determine the y-intercept of a line on a graph?

• It is the point where the line crosses the y-axis

• It is the lowest point on the line

• It is the point where the line crosses the x-axis

• It is the highest point on the line

What is the slope of a line that represents a constant rate of fuel consumption?

• Positive

• Negative

• Zero

• Undefined

In the context of a cable service, what does the y-intercept represent for new customers?

• The cost per channel

• The monthly service fee

• The total cost after one year

• The one-time service fee