Real-Life Slopes: Write Equations & Compare Rates

1. Sarah and Tom are biking. Sarah's distance from home can be represented by the equation y = 3x, while Tom's distance is represented by y = 2x + 5. Write the equations for both and identify who is biking faster based on their slopes.

• Tom is biking faster than Sarah.

• Sarah's speed is equal to Tom's speed.

• Sarah is biking faster than Tom.

• Both are biking at the same speed.

2. A car travels at a speed of 60 miles per hour, while a motorcycle travels at 45 miles per hour. If both start from the same point, write the equations for their distances over time and compare their slopes to determine who travels faster.

• The car travels faster than the motorcycle.

• The car and motorcycle have equal distances over time.

• The motorcycle travels faster than the car.

• Both vehicles travel at the same speed.

3. A gardener plants two types of flowers. The first type grows at a rate of 4 inches per week, while the second type grows at 2 inches per week. Write the equations for their heights over time and identify which flower grows faster by comparing the slopes.

• The second type of flower grows faster.

• Both flowers grow at the same rate.

• The first type of flower grows faster.

• The first type grows at 6 inches per week.

4. A train travels 80 miles in 2 hours, while a bus travels 50 miles in 1.5 hours. Write the equations for their speeds and determine which vehicle has a steeper slope on a distance-time graph.

• The train has a steeper slope on the distance-time graph.

• The bus has a steeper slope on the distance-time graph.

• Both vehicles have the same slope on the distance-time graph.

• The train and bus cannot be compared on a distance-time graph.

5. Emily saves $5 each week, while her friend saves $3 each week. Write the equations for their savings over time and compare the slopes to see who saves money faster.

• Emily saves money faster than her friend.

• Emily saves $3 more than her friend each week.

• Emily and her friend save the same amount each week.

• Emily saves money slower than her friend.

6. A runner completes a 5K race in 25 minutes, while another runner completes it in 30 minutes. Write the equations for their speeds and identify who has a greater slope on a distance-time graph.

• The first runner has a lower slope.

• The second runner has a greater slope.

• Both runners have the same slope.

• The first runner has a greater slope.

7. A factory produces 100 toys in 4 hours, while another factory produces 150 toys in 6 hours. Write the equations for their production rates and compare the slopes to see which factory is more efficient.

• Factory A produces 30 toys per hour.

• Factory A produces 100 toys in 5 hours.

• Both factories are equally efficient with a production rate of 25 toys per hour.

• Factory B is more efficient with 35 toys per hour.

8. A cyclist rides at a speed of 15 miles per hour, while a jogger runs at 6 miles per hour. Write the equations for their distances over time and determine who is moving faster by comparing the slopes.

• Both are moving at the same speed.

• The cyclist is moving faster.

• The cyclist and jogger have equal distances over time.

• The jogger is moving faster.

9. A student reads 20 pages in 1 hour, while another student reads 15 pages in 1 hour. Write the equations for their reading rates and compare the slopes to see who reads faster.

• The first student reads faster.

• The second student reads faster.

• The first student reads slower.

• Both students read at the same rate.

10. A chef prepares 10 dishes in 2 hours, while another chef prepares 8 dishes in 2 hours. Write the equations for their cooking rates and identify which chef has a steeper slope on a graph.

• Chef 1 has a steeper slope.

• Both chefs have the same slope.

• Chef 1 prepares more dishes overall.

• Chef 2 has a steeper slope.