Proportions, Ratios, and Percent

A car travels 150 miles in 3 hours. What is the unit rate of the car's speed in miles per hour?

• 45 miles per hour

• 50 miles per hour

• 55 miles per hour

• 60 miles per hour

Answer explanation

To find the unit rate, divide the total distance by the total time. 150 miles ÷ 3 hours = 50 miles per hour. Therefore, the car's speed is 50 miles per hour.

Tags

CCSS.8.EE.B.5

Which of the following graphs represents a proportional relationship with a unit rate of 3?

• A line passing through (0,0) and (1,2)

• A line passing through (0,0) and (1,3)

• A line passing through (0,0) and (2,3)

• A line passing through (0,0) and (3,3)

Answer explanation

A proportional relationship has a constant unit rate. The line through (0,0) and (1,3) has a slope of 3, indicating a unit rate of 3. The other options do not have this unit rate.

Tags

CCSS.8.EE.B.5

• 2

• 4

• 6

• 8

Answer explanation

The slope of a line in the equation y = mx + b is represented by 'm'. In this case, the equation is y = 4x + 2, so the slope (m) is 4. Therefore, the correct answer is 4.

Tags

CCSS.8.EE.B.6

• They are parallel

• They are perpendicular

• They intersect at the origin

• They are the same line

Answer explanation

The equations y = 2x and y = 2x + 3 have the same slope (2) but different y-intercepts. This means they are parallel lines, as they will never intersect.

Tags

CCSS.8.EE.B.6

A recipe requires 2 cups of sugar for every 5 cups of flour. What is the ratio of sugar to flour?

• 2:5

• 5:2

• 1:2.5

• 2.5:1

Answer explanation

The recipe states 2 cups of sugar for every 5 cups of flour. This directly gives the ratio of sugar to flour as 2:5, making the correct answer 2:5.

Tags

CCSS.8.EE.B.5

Answer explanation

The equation y = \frac{1}{2}x + 1 has a slope of \frac{1}{2}, which matches the requirement. The other options have different slopes: 2, 1, and \frac{1}{3}, respectively.

Tags

CCSS.8.EE.B.6

A line passes through the points (1, 2) and (3, 6). What is the slope of the line?

• 1

• 2

• 3

• 4

Answer explanation

To find the slope (m) of the line through points (1, 2) and (3, 6), use the formula m = (y2 - y1) / (x2 - x1). Here, m = (6 - 2) / (3 - 1) = 4 / 2 = 2. Thus, the slope is 2.

Tags

CCSS.8.EE.B.6

If a line has a slope of 5 and passes through the origin, what is its equation?

Answer explanation

The equation of a line in slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept. Since the slope is 5 and it passes through the origin (0,0), the equation is y = 5x.

Tags

CCSS.8.EE.B.6

A store is having a 20% off sale. If an item originally costs $50, what is the sale price?

• $30

• $35

• $40

• $45

Answer explanation

To find the sale price, calculate 20% of $50, which is $10. Subtract this from the original price: $50 - $10 = $40. Therefore, the sale price is $40.

Tags

CCSS.8.EE.B.5

Which of the following represents a proportional relationship?

Answer explanation

A proportional relationship is defined by the equation y = kx, where k is a constant. The equation y = 3x fits this definition, as it shows a constant ratio between y and x. The other options include constants or non-linear terms.

Tags

CCSS.8.EE.B.5