Graphing Linear Equations: Slope and Real-World Contexts

A car travels at a constant speed of 60 miles per hour. Graph the linear equation that represents the distance traveled over time. What is the slope of the graph?

• 60 miles per hour

• 120 miles per hour

• 90 miles per hour

• 30 miles per hour

A bike rental shop charges a flat fee of $10 plus $2 for every hour rented. Write the equation that represents the total cost (C) in terms of hours (h) rented. What does the slope represent in this context?

• C = 10h + 2; the slope represents the total cost of renting the bike.

• C = 2h; the slope represents the initial fee for renting the bike.

• C = 10 + 5h; the slope represents the discount per hour of renting the bike.

• C = 10 + 2h; the slope represents the cost per hour of renting the bike.

A student is saving money for a new video game. If they save $5 each week, graph the equation representing their savings over time. What is the slope of the graph?

• 2

• 5

• 0

• 10

A train travels 150 miles in 3 hours. Write the equation of the line that represents the train's distance over time. What does the slope indicate about the train's speed?

• y = 30x; the slope indicates the train's speed is 30 miles per hour.

• y = 50x; the slope indicates the train's speed is 50 miles per hour.

• y = 75x; the slope indicates the train's speed is 75 miles per hour.

• y = 100x; the slope indicates the train's speed is 100 miles per hour.

A gardener plants flowers in a straight line. If the first flower is planted at (1, 2) and the second at (4, 8), write the equation of the line that represents the height of the flowers over distance. What is the slope?

• y = 4x - 2; slope = 4

• y = 2x; slope = 2

• y = 3x; slope = 3

• y = x + 1; slope = 1

A phone company offers a plan that costs $30 per month plus $0.10 per minute of calls. Graph the total cost (C) as a function of minutes (m) used. What does the slope of the graph represent?

• The slope of the graph represents the total monthly cost of the plan.

• The slope of the graph represents the fixed cost of the plan, which is $30.

• The slope of the graph represents the total number of minutes used.

• The slope of the graph represents the cost per minute of calls, which is $0.10.

A runner completes a 5K race in 25 minutes. Write the equation that represents the distance covered over time. What is the slope of the graph, and what does it signify?

• d(t) = 10t; slope = 10 km/h

• d(t) = 15t; slope = 15 km/h

• d(t) = 12t; slope = 12 km/h

• d(t) = 5t; slope = 5 km/h

A restaurant's revenue increases by $200 for every additional table they set up. If they start with a revenue of $1,000, write the equation for their revenue (R) based on the number of tables (t). What does the slope tell you?

• R = 200t

• R = 1000 + 200t

• R = 1000 - 200t

• R = 1000 + 100t

A student is studying for a test and practices for 2 hours a day. If they start with 10 hours of study time, graph the total study time over days. What is the slope of the graph?

• 5

• 1

• 3

• 2

A delivery service charges a base fee of $5 plus $1.50 per mile. Write the equation for the total cost (C) based on the distance (d) in miles. What does the slope represent in this scenario?

• C = 5 + 2d; the slope represents the total cost.

• C = 1.50 + 5d; the slope represents the base fee.

• C = 5 + 1.50d; the slope represents the cost per mile.

• C = 1.50d; the slope represents the distance traveled.