Understanding Slope in Linear Equations: Grade 8 Challenge

A car rental company charges a flat fee of $50 plus $0.20 per mile driven. Write a linear equation to represent the total cost (C) in terms of miles driven (m). What is the slope of this equation and what does it represent in this context?

• C = 50 + 0.10m; slope = 0.10, representing the cost of fuel per mile.

• C = 50 + 0.20m; slope = 0.20, representing the cost per mile.

• C = 50 + 0.50m; slope = 0.50, representing the total cost of the car rental.

• C = 50 - 0.20m; slope = -0.20, representing a discount per mile.

A gardener is planting flowers in a straight line. If he plants 5 flowers in 2 hours, what is the slope of the line representing the number of flowers planted over time? Write the equation in slope-intercept form.

• y = 2.5x

• y = 10x

• y = 1.5x

• y = 5x

A phone plan costs $30 per month plus $0.10 per text message. Write the equation for the total cost (C) based on the number of text messages (t) sent. What does the slope represent in this scenario?

• C = 30t + 0.10; the slope represents the total monthly cost.

• C = 30 + 0.05t; the slope represents the number of text messages sent.

• C = 0.10 + 30t; the slope represents the fixed cost of the plan.

• C = 30 + 0.10t; the slope (0.10) represents the cost per text message.

A student scores 80 points on a test and increases their score by 5 points for each additional hour of study. Write a linear equation to represent the student's score (S) based on hours studied (h). What is the slope and its interpretation?

• S = 80 - 5h; Slope = -5

• S = 80 + 5h; Slope = 5

• S = 80 + 10h; Slope = 10

• S = 75 + 5h; Slope = 5

A bike rental shop charges a one-time fee of $15 and $5 for each hour of rental. Write the equation for the total cost (C) based on hours rented (h). What does the slope indicate about the cost?

• C = 5h; The slope indicates that the cost remains constant regardless of hours rented.

• C = 15 + 10h; The slope indicates that the cost decreases by $10 for each additional hour rented.

• C = 15 + 5h; The slope indicates that the cost increases by $5 for each additional hour rented.

• C = 15h; The slope indicates that the cost increases by $15 for each additional hour rented.

A factory produces 100 units of a product in 4 hours. If the production rate remains constant, what is the slope of the line representing units produced over time? Write the equation in standard form.

• 25x - y = 0

• 25x + y = 100

• 30x - y = 0

• 20x - y = 0

A delivery service charges a base fee of $10 plus $2 for each mile driven. Write the equation for the total charge (C) based on miles driven (m). What does the slope represent in this context?

• C = 10 + 3m; the slope represents the base fee per mile.

• C = 10 + 2m; the slope represents the cost per mile driven.

• C = 5 + 2m; the slope represents the delivery time per mile.

• C = 10 + 5m; the slope represents the total distance driven.

A student is saving money for a new video game. If they save $15 each week, write a linear equation to represent the total savings (S) after w weeks. What is the slope and what does it mean?

• S = 15w + 5; slope = 15, meaning the student saves $15 plus a bonus of $5 each week.

• S = 20w; slope = 20, meaning the student saves $20 each week.

• S = 10w; slope = 10, meaning the student saves $10 each week.

• S = 15w; slope = 15, meaning the student saves $15 each week.

A restaurant's revenue increases by $200 for every additional table they add. Write a linear equation to represent the revenue (R) based on the number of tables (t). What does the slope indicate about the restaurant's revenue?

• R = 100t; the slope indicates that revenue decreases by $100 for each additional table.

• R = 300t; the slope indicates that revenue remains constant regardless of the number of tables.

• R = 200t + 500; the slope indicates that revenue increases by $500 for each additional table.

• R = 200t; the slope indicates that revenue increases by $200 for each additional table.

A train travels at a constant speed of 60 miles per hour. Write an equation to represent the distance (d) traveled in terms of time (t). What is the slope and how does it relate to the train's speed?

• d = 60t; slope = 60 (train's speed in mph)

• d = 60t + 10; slope = 60

• d = 30t; slope = 30

• d = 60t^2; slope = 120t