Slope and Intercept: Real-World Line Challenges

A car rental company charges a flat fee of $20 plus $0.15 per mile driven. Write the equation in slope-intercept form that represents the total cost (C) as a function of miles driven (m). What is the slope of this equation?

• The slope of the equation is 0.10.

• The slope of the equation is 0.20.

• The slope of the equation is 1.5.

• The slope of the equation is 0.15.

A gardener is planting a row of trees. The first tree is planted at the point (0, 2) and the second tree at (4, 10). What is the slope of the line connecting these two trees? Is this line parallel to a line with a slope of 2?

• The slope is 2 and it is perpendicular to a line with a slope of 2.

• The slope is 3 and it is not parallel to a line with a slope of 2.

• Yes, the slope is 2 and it is parallel to a line with a slope of 2.

• The slope is 1 and it is parallel to a line with a slope of 2.

Tags

CCSS.8.EE.B.6

A delivery truck travels at a constant speed, represented by the equation y = 50x + 100, where y is the distance in miles and x is the time in hours. What does the slope represent in this context?

• The slope represents the speed of the delivery truck, which is 50 miles per hour.

• The slope shows the maximum distance the truck can travel.

• The slope indicates the time taken to travel a mile.

• The slope represents the total distance traveled by the truck.

Tags

CCSS.HSF.LE.B.5

Two friends are walking in the park. One walks at a rate of 3 feet per second, and the other walks at a rate of 5 feet per second. Write the equations for both friends' distances over time. Are their paths parallel or perpendicular?

• Their paths intersect at a right angle.

• One friend walks faster than the other.

• Their paths are parallel.

• Their paths are perpendicular.

A bike path is represented by the equation y = -1/2x + 6. If another bike path is represented by y = 2x - 4, are these paths parallel, perpendicular, or neither? Explain your reasoning.

• neither

• perpendicular

• coincident

• parallel

Tags

CCSS.8.EE.B.5

A company’s profit can be modeled by the equation P = 150x - 300, where P is the profit in dollars and x is the number of items sold. What is the slope of this equation, and what does it represent in a real-world context?

• -150

• 150

• 300

• 1500

Tags

CCSS.HSF.LE.B.5

A line passes through the points (1, 3) and (3, 7). Calculate the slope of the line and write its equation in slope-intercept form. Is this line perpendicular to a line with a slope of -1/2?

• The slope of the line is 1, and its equation is y = x + 2. No, this line is not perpendicular to a line with a slope of -1/2.

• The slope of the line is 3, and its equation is y = 3x - 2. Yes, this line is perpendicular to a line with a slope of -1/2.

• The slope of the line is 0, and its equation is y = 3. Yes, this line is perpendicular to a line with a slope of -1/2.

• The slope of the line is 2, and its equation is y = 2x + 1. Yes, this line is perpendicular to a line with a slope of -1/2.

Tags

CCSS.8.EE.B.6

A student is analyzing the relationship between study time and test scores. If the equation of the line is y = 5x + 60, what does the slope indicate about the relationship? How would you find a line that is parallel to this one?

• The slope indicates a weak relationship; a parallel line has a slope of 10.

• The slope indicates no relationship; a parallel line has a slope of 0.

• The slope indicates a positive relationship; a parallel line has the same slope of 5.

• The slope indicates a negative relationship; a parallel line has a slope of -5.

Tags

CCSS.8.EE.B.5