Linear Relationships and Rates of Change

The video covers understanding and representing proportional and linear relationships using graphs, tables, and equations. It explains how to calculate slope, interpret graphs, and find solutions to linear equations. Key examples include jogging speeds, blueberry costs, and various mathematical problems to illustrate these concepts.

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?

• 4 miles

• 8 miles

• 12 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

• 20

• 25

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

• 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?

• Total cost

• Hourly labor rate

• Number of hours

• Cost of supplies

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

• The price per muffin

• The delivery charge

• The number of muffins delivered

• The total cost of muffins

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?

• 2 cups

• 6 cups

• 4 cups

• 3 cups

If a plane is cruising at a constant altitude, what is the slope of the line representing its elevation over time?

• Zero

• Negative

• Undefined

• Positive

How much does each turkey sandwich add to the cost of delivery if one office pays $33 for 4 sandwiches and another pays $61 for 8 sandwiches?

• $8

• $7

• $6

• $5

What is the y-intercept of the equation y = 70x + 100, representing a cable service fee for new customers?

• $100

• $70

• $0

• $170