Understanding Rates of Change and Linear Relationships

This video tutorial covers the concept of rate of change in linear relationships, explaining how it is represented as the slope of a graph. It includes practice problems on proportional relationships, such as calculating calories from grams of fish and money from raffle tickets. The video also explores how to compare slopes and graph lines using equations, providing a comprehensive understanding of these mathematical concepts.

What is the rate of change in a linear relationship?

• The total change in x over the total change in y

• The amount y changes when x increases by 1

• The amount x changes when y increases by 1

• The total change in y over the total change in x

In the example of earnings over time, what is the rate of change?

• $15 per hour

• $10 per hour

• $25 per hour

• $20 per hour

What equation represents the relationship between calories and grams of fish?

• y = 2x

• y = 3x

• y = 0.5x

• y = 1.5x

If 100 grams of fish have 150 calories, how many calories are in 10 grams?

• 10 calories

• 15 calories

• 20 calories

• 25 calories

What is the simplified form of the ratio 24/10?

• 12/5

• 24/5

• 6/5

• 48/10

How much money is collected for selling 10 raffle tickets?

• $12

• $36

• $48

• $24

What does it mean if a line's slope is greater than one?

• The line is horizontal

• The vertical length is shorter than the horizontal length

• The vertical length is equal to the horizontal length

• The vertical length is greater than the horizontal length

What is the slope of a line if the horizontal length is 4 and the vertical length is 4?

• 0

• 0.5

• 2

• 1

What are the coordinates of a point on the line y = 3/11(x - 2) when x = 13?

• (11, 2)

• (13, 3)

• (13, 2)

• (11, 3)

How do you find the y-value when x = 2 in the equation y = 3/11(x - 2)?

• Multiply 3/11 by (2 - 2)

• Subtract 2 from 3/11

• Add 2 to 3/11

• Multiply 3/11 by 2