Real-Life Slope Comparisons: Who’s Steeper?

A car travels at a speed of 60 miles per hour. Another car travels at 75 miles per hour. Compare the slopes of their distance-time graphs. Which car has a steeper slope?

• The car traveling at 75 miles per hour has a shallower slope.

• Both cars have the same slope.

• The car traveling at 75 miles per hour has a steeper slope.

• The car traveling at 60 miles per hour has a steeper slope.

A hiker climbs a hill that rises 300 feet over a distance of 1 mile. Another hiker climbs a hill that rises 450 feet over a distance of 1.5 miles. Which hiker has a steeper slope?

• The second hiker has a steeper slope.

• Both hikers have the same slope.

• The first hiker has a gentler slope.

• The first hiker has a steeper slope.

A bike path rises 2 feet for every 10 feet traveled horizontally. A walking path rises 3 feet for every 15 feet traveled horizontally. Compare the slopes of the two paths. Which path is steeper?

• The bike path has a slope of 0.2 while the walking path has a slope of 0.3.

• The walking path is steeper than the bike path.

• Both paths have the same slope; neither is steeper.

• The bike path is steeper than the walking path.

A train travels 120 miles in 2 hours, while a bus travels 90 miles in 1.5 hours. Determine the slopes of their distance-time graphs and identify which mode of transportation is faster.

• The train travels at 70 miles per hour.

• Both the train and the bus travel at the same speed of 60 miles per hour.

• The train is faster than the bus at 80 miles per hour.

• The bus travels at 50 miles per hour.

A ramp rises 4 feet over a horizontal distance of 20 feet. Another ramp rises 6 feet over a horizontal distance of 30 feet. Compare the slopes of the ramps. Which ramp is steeper?

• The second ramp is steeper.

• The slopes of the ramps cannot be compared.

• Both ramps are equally steep.

• The first ramp is steeper.

A skateboarder goes down a ramp that descends 5 feet over a distance of 10 feet. Another skateboarder goes down a ramp that descends 8 feet over a distance of 15 feet. Which skateboarder experiences a steeper slope?

• The first skateboarder experiences a steeper slope.

• Neither skateboarder experiences a slope.

• The second skateboarder experiences a steeper slope.

• Both skateboarders experience the same slope.

A road rises 200 feet over a distance of 1 mile. Another road rises 150 feet over a distance of 0.5 miles. Compare the slopes of the two roads. Which road has a steeper incline?

• The second road has a steeper incline.

• The second road has a gentler slope.

• The first road has a steeper incline.

• Both roads have the same incline.

A water slide descends 10 feet over a horizontal distance of 25 feet. Another slide descends 15 feet over a horizontal distance of 30 feet. Which slide has a steeper slope?

• The second slide is less steep than the first.

• The second slide has a steeper slope.

• The first slide has a steeper slope.

• Both slides have the same slope.

A mountain trail rises 500 feet over 2 miles, while a different trail rises 300 feet over 1 mile. Compare the slopes of the two trails. Which trail is steeper?

• The first trail is steeper.

• Both trails have the same slope.

• The second trail is less steep than the first.

• The second trail is steeper.

A construction ramp rises 12 feet over a distance of 40 feet. Another ramp rises 15 feet over a distance of 50 feet. Determine which ramp has a steeper slope.

• Both ramps have the same slope.

• The first ramp has a slope of 0.3 and the second ramp has a slope of 0.4.

• The second ramp is steeper than the first ramp.

• The first ramp is steeper than the second ramp.