Calculating Slope
A line rises 4 units and runs 8 units. What is its slope?
(Fraction, Decimal, Percent)
1/2, 0.5, 50%
Which is steeper: slope of ¼ or slope of ⅖?
2/5
If a slope is 1/1, what angle does it make with the ground?
45 degrees
A taxi charges $3 per km. What is the slope of the cost vs. distance graph?
3 ($/km)
Give one example of slope in everyday life.
→ Examples: wheelchair ramp, driveway, road, roof, slide.
A ramp rises 2 meters over a run of 20 meters. Express the slope as a percent.
10%
Hill A has slope 10%. Hill B has slope ⅛. Which is steeper?
Hill B = 12.5%
A ramp rises 1.5 m over a run of 12 m. What is the angle of elevation?
7 degrees
A tank drains 12 L per minute. What does the slope represent?
12 L/min (water decreases by 12 each minute)
Why is slope important when designing a wheelchair ramp?
→ To ensure safety and accessibility (gentle enough for users).
A roof has a slope of ⅖. Write it as a decimal and a percent.
.4, 40%
A wheelchair ramp has a slope of 1/12. A slide has a slope of 1/8. Which is safer for accessibility?
1/12 = Less steep
A roof has an angle of 40°. What is its slope as a decimal?
0.84 (Tan(40))
A runner covers 18 km in 2 hours. What is the slope of the distance-time graph?
→ 9 km/h
You’re building a roof. Why does knowing slope matter?
→ It helps shed water/snow and prevent weather damage.
A line has slope 3/7. If the rise is 15, what is the run?
35
Road A rises 80 m over 400 m. Road B rises 150 m over 700 m. Which is steeper?
Road B
A ladder leans against a wall with rise 9 ft and run 5 ft. What is the angle with the ground?
61 degrees
A phone battery drops from 100% to 70% in 90 minutes. What is the slope?
→ ≈ -0.33%/min
Engineers design a road with slope less than 8%. If it rises 50 m, what’s the minimum run?
→ 625 m
A ski hill rises 120 m and runs 450 m. Write the slope as a fraction, decimal, and percent.
4/15, 0.267, 26.7%
Compare slopes 0.25, 35%, and 2/7. Order least to most steep.
0.25 < 2/7 ≈ 0.286 < 35% (0.35)
A hiking trail rises 600 m over a run of 2.5 km. What is the angle of elevation?
14 degrees
A student invests $200. After 6 months, it’s worth $260. If it grows steadily, when will it reach $400?
→ 20 months
You are designing a ski slope that qualifies as “intermediate” (25–40%). Suggest rise and run.
→ Example: Rise 300 m, Run 1000 m → 30% slope (valid answer).