Proportional Relationships

Which linear function shows a direct variation?

• 
• 
• 
• 

Which set represents a direct variation? (x,y)

• (4,7) (6,9) (8,11) (10,13)

• (4,12) (6,18) (8,24) (10,30)

• (4,1) (6,3) (8,5) (10,7)

• (4,3) (6,3) (8,3) (10,3)

Which describes whether the relationship between the earnings and the number of hours represents a direct variation?

Caleb’s Earnings

Hours

12    15    18   21

Earnings(in dollars)

140   170   200   230

• He earns 20 more than 10 times the number of hours he works each week, so the earnings vary directly with the hours.

• The earnings increase by 30 for every increase of 3 hours, so the earnings vary directly with the hours.

• The ratios of earnings to hours are not the same each week, so the earnings do not vary directly with the hours.

• The earnings increase at a steady rate, so the earnings do not vary directly with the hours.

Which explains whether or not the graph represents a direct variation?

• The graph has a constant of variation of 3, so it represents a direct variation.

• The graph has a slope of 3, so it represents a direct variation.

• The graph has a positive slope, so it does not represent a direct variation.

• The graph does not begin at the origin, so it does not represent a direct variation.

Lydia writes the equation below with a missing value.

y=5x - ( )

She puts a value in the ( ) and says that the equation represents a direct variation. Which explains whether the equation could represent a direct variation?

• If she puts 0 in the box she would have a direct variation.

• If she puts 5 in the box she would have a direct variation.

• The equation is not of the form , so it cannot represent a direct variation.

• The equation has a minus sign, so it cannot represent a direct variation.

Given that "y" varies directly with "x" below, what is the value of "y" if the value of "x" is 7?

(x,y) = (2,12) (4,24) (6,36) (10,60)

• 37

• 42

• 58

• 64

The number of milligrams of a certain medicine a veterinarian gives to a dog varies directly with the weight of the dog. If the veterinarian gives a 30-pound dog milligram of the medicine, which equation relates the weight, w, and the dosage, d?

• $d=\frac{1}{50}w$

• $d=\frac{3}{5}w$

• $d=18w$

• $d=50w$

The length of a spring varies directly with the mass of an object that is attached to it. When a 30-gram object is attached, the spring stretches 9 centimeters. Which equation relates the mass of the object, m, and the length of the spring, s?

• $s=\frac{3}{10}m$

• $s=\frac{3}{10}m$

• $m=\frac{3}{10}s$

• $m=\frac{10}{3}s$

Which graph or equation represents a nonproportional relationship?

• 
• 
• $y=0.375x$

• $y=\frac{5}{9}x$

 $\frac{10x}{3y}=1$  

Which statement correctly compares the constants of variation for the graph and the equation below?

• The graph has a greater constant of variation.

• The equation has a greater constant of variation.

• The constant of variation is the same for the graph and the equation.

• The constant of variation cannot be compared because the equation is nonproportional.