3.5 Math 8 CBA Review

Which equation represents a non-proportional relationship between x and y?

• y = 10x

• y = -2x

• y = 5(x + 3)

Answer explanation

The equation y = 5(x + 3) represents a non-proportional relationship because it includes a constant term (3) that shifts the line, unlike the other equations which pass through the origin.

The cost for water usage varies directly with the number of gallons of water used. The cost for using 1,250 gallons of water was $75.00. What was the cost for using 900 gallons of water?

• $54.00

• $67.50

• $60.00

• $45.00

Answer explanation

The cost per gallon is $75.00 / 1250 gallons = $0.06 per gallon. For 900 gallons, the cost is 900 * $0.06 = $54.00. Thus, the correct answer is $54.00.

Which situation could NOT represent a proportional relationship?

• The number of pages in a book if there are 15 pages per chapter

• The distance traveled by a car moving at a constant speed of 60 miles per hour over time

• The total cost of buying groceries if there is a $5 delivery fee added to each purchase

• The total amount of paint needed for a project if each wall requires 2 gallons of paint

Answer explanation

The total cost of groceries includes a fixed $5 delivery fee, making it a non-proportional relationship. In contrast, the other options represent direct proportionality based on consistent rates.

The graph shows the relationship between the cost of some almonds and the weight of the almonds in pounds. Which function best represents the relationship shown in the graph?

• y = 5x

• y = 20x

• y = 4x

• y = 1/5x

Answer explanation

The graph indicates a linear relationship between cost and weight. The correct function, y = 4x, suggests that for every pound of almonds, the cost is $4, which aligns with the graph's slope.

The graph of a linear function is shown on the coordinate grid. What is the y-intercept of the graph of the linear function?

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Triangle MNP and triangle JKL are similar right triangles. Which proportion can be used to show that the slope of JL is equal to the slope of MP?

Answer explanation

The correct proportion is \(\frac{-4-6}{-6-9}=\frac{-2-2}{-3-3}\) because it compares the vertical and horizontal changes of segments JL and MP, confirming their slopes are equal due to the similarity of triangles MNP and JKL.

Maddy has 8 barbies in her toy box, and she adds 1 new barbie every month. Based on this information, which representation best shows this relationship between the number of barbies Maddy has in her toy box, y, and the number of months that have passed, x?

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• y=8x + 1

Triangle DEF and triangle GHI are similar right triangles. Based on this information, which statement is true?

• The relationship between the slope of the hypotenuse of triangle DEF and the slope of the hypotenuse of triangle GHI cannot be determined.

• The slope of the hypotenuse of triangle DEF is equal to the slope of the hypotenuse of triangle GHI.

• The slope of the hypotenuse of triangle DEF is less than the slope of the hypotenuse of triangle GHI.

• The slope of the hypotenuse of triangle DEF is greater than the slope of the hypotenuse of triangle GHI.

Answer explanation

Since triangles DEF and GHI are similar right triangles, their corresponding angles are equal. This means the slopes of their hypotenuses, which depend on the angles, are also equal.

Which sets of ordered pairs represents y as a function of x? Select two

• { (1.5, 2.0), (2.5, 3.0), (3.5, 4.0), (-2.5, 3.0)}

• { (0.1, 0.2), (0.2, 0.3), (0.3, 0.4), (0.4, 0.5) }

• { (2, 3.5), (3, 4.5), (1, 3.5), (3, -4.5)}

• { (1, -1), (2, 2), (3, 3), (2,4)}

Answer explanation

The first set has unique x-values, making it a function. The second set also has unique x-values. The third and fourth sets have repeated x-values (3 and 2), which disqualifies them as functions.

Answer explanation

Alex completes 3 paintings in 0.5 hours, so in 1 hour he completes 6 paintings. In 4 hours, he can complete 6 x 4 = 24 paintings.