Algebra (8th Grade) - Proportional Relationships -

A painter made the table below to show the amount of paint it takes to cover a certain amount of square feet. The amount of paint varies directly with the area of each wall. Amount of Paint & Size of Wall ------------------------------------- Area of Wall, x | Amount of paint, y (ft2) | (pints) 64 | 4 144 | 9 400 | 25 How much paint should the painter expect to use to paint a wall with an area of 256 square feet? A) 16 pints B) 32 pints C) 128 pints D) 225 pints

A) 16 pints

Which explains whether or not the graph represents a direct variation? A) The graph has a constant of variation of 3, so it represents a direct variation. B) The graph has a slope of 3, so it represents a direct variation. C) The graph has a positive slope, so it does not represent a direct variation. D) The graph does not begin at the origin, so it does not represent a direct variation.

A) The graph has a variation of 3, so it represents a direct variation.

A person weighs a different amount on other surfaces in space than they do on Earth because the gravitational pull of each surface is different than that of Earth. The table and graph show the weights of objects on Earth, Mars, and the Moon. If a person weighs 240 pounds on Earth, what would be the difference in weight of the same person on Mars and on the Moon (based on the table and graph)? A) The person weighs 56 pounds more on Mars than on the Moon. B) The person weighs 56 pounds more on the Moon than on Mars. C) The person weighs 560 pounds more on Mars than on the Moon. D) The person weighs 560 pounds more on the Moon than on Mars.

A) The person weighs 56 pounds more on Mars than on the Moon.

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? A) d = 1 / 50 w B) d = 3 / 5 w C) d = 18w D) d = 50w

A) d = 1 / 50 w

The table shows the number of minutes Jalen talks on his mobile phone and the cost of the phone calls. Jalen's Mobile Phone Cost -------------------------------------- # of minutes, x | Cost, y 150 | $7.50 220 | $11.00 250 | $12.50 275 | $13.75 If the cost varies directly with the number of minutes Jalen talks on the phone, which equation represents the variation? A) y = 0.05x B) y = 20x C) y = 157.5x D) y = 1125x

A) y = 0.05x

A botanist uses the representations below to show the heights in inches, h, of different plants over a period of time, t. Plant A ------------------------------ Time in weeks, t | Height in inches,h 60 | 90 80 | 120 100 | 150 120 | 180 Plant B ------------------ h = 4t / 3 Plant C ------------------- graph.image If the growth patterns continue, how much taller is the tallest plant than the shortest plant at 120 weeks of growth? A) 180 inches B) 200 inches C) 270 inches D) 280 inches

B) 200 inches

A veterinarian knows that a 50-pound dog gets 0.5 milligram of a certain medicine, and that the number of milligrams, m, varies directly with the weight of the dog, w. The vet uses these steps to find the amount of medicine to give a 10-pound dog. Step 1 : Find the constant of variation. k = 0.5 / 50 = 0.01 Step 2 : Write the direct variation equation. m = 0.01w Step 3 : Substitute 10 into the equation to find the dosage for a 10-pound dog. 10 = 0.01w Step 4 : Solve for w 10 = 0.01w w = 1000 .The 10-pound dog needs 1000 milligrams. In which step did the veterinarian make the first error? A) Step 1 B) Step 2 C) Step 3 D) Step 4

C) Step 3

Caleb made the table below to show the number of hours he works and the amounts he earns over a four-week period. Caleb's Earnings ------------------------------------- Hours | Earnings (in dollars) 12 | 140 15 | 170 18 | 200 21 | 230 Which describes whether the relationship between the earnings and the number of hours represents a direct variation? A) He earns 20 more than 10 times the number of hours he works each week, so the earnings vary directly with the hours. B) The earnings increase by 30 for every increase of 3 hours, so the earnings vary directly with the hours. C) The ratios of earnings to hours are not the same each week, so the earnings do not vary directly with the hours. D) The earnings increase at a steady rate, so the earnings do not vary directly with the hours.

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

Which representation has a constant of variation of -2.5? A ---------------------- x ! Y -2 ! -5 -3 ! -7.5 -4 ! -10 -5 ! -12.5 B --------------------- X ! Y 4 ! -10 6 ! -15 8 ! -20 10 ! -25 C -------------- y= -2.5x + 1 D -------------------- image.graph A) A B) B C) C D) D

I sadly don't truely know the answer... BUT! I know for sure that it is NOT A) A Trust me i found out the hard way. Heheh...

Which table represents a direct variation? A) Table A B) Table B C) Table C D) Table D

Sadly I dont know the true answer, BUT ! It is definitly NOT D) Table D found out the hard way.