Linear Relationships and Functions

This video tutorial covers 8th-grade mathematics, focusing on representing proportional relationships. It explains the rate of change in linear relationships, using graphs to illustrate concepts. Practice problems include analyzing proportional relationships between calories and grams of fish, calculating money from selling raffle tickets, and determining slopes. The video concludes with graphing equations and a call to action for viewer engagement.

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

• 20 dollars per hour

• 25 dollars per hour

• 10 dollars per hour

• 15 dollars per hour

Why does the graph start at 10 dollars when x is 0 hours?

• Because 10 dollars is the maximum value

• Because it represents an initial value of 10 dollars

• Because the rate of change is 10 dollars per hour

• Because the graph is incorrect

If x represents grams of fish and y represents calories, what equation represents the relationship if y is 1.5 times x?

• y = x

• y = 2x

• y = 1.5x

• y = 0.5x

How many calories are in 1000 grams of fish if y is 1.5 times x?

• 1000 calories

• 2000 calories

• 1500 calories

• 2500 calories

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

• 5/12

• 24/5

• 6/5

• 12/5

If students collect $24 for every 10 raffle tickets sold, what is the equation relating money collected (m) to tickets sold (r)?

• m = 12/5r

• m = 2.4r

• m = 24r

• m = 10r

What is the slope of a line if the vertical side of a triangle is 6 units and the horizontal side is 4 units?

• 1

• 2/3

• 3/2

• 1/2

How can you tell if a line's slope is greater than one?

• The vertical length is greater than the horizontal length

• The line is horizontal

• The vertical length is equal to the horizontal length

• The vertical length is shorter than the horizontal length

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

• (3, 13)

• (11, 3)

• (13, 11)

• (13, 3)

If the slope of a line is 1/3, what can be said about the vertical and horizontal lengths?

• The line is vertical

• 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