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📈 Chapter 13: Two Variables, One Line • Exercise Set 13.3

Verified step-by-step solutions for your class notes.

Exercise Set 13.1 3Exercise Set 13.2 4Exercise Set 13.3 3Exercise Set 13.4 3Exercise Set 13.5 6End-of-Chapter Exercises 6All Exercises 25
Q1

The following diagrams represent ski hills. Rank the hills in order of their steepness, from least to greatest.

  • Hill A: Rise = 60m, Run = 70m
  • Hill B: Rise = 60m, Run = 110m
  • Hill C: Rise = 80m, Run = 100m
Run = 70 m 60 m Hill A Run = 110 m 60 m Hill B Run = 100 m 80 m Hill C
Ski Hills Comparison: Hill A (Slope ≈ 0.857), Hill B (Slope ≈ 0.545), Hill C (Slope = 0.800)

Answer: Steepness is determined by the slope (Rise / Run).
Slope of A = $60 / 70 \approx 0.857$
Slope of B = $60 / 110 \approx 0.545$
Slope of C = $80 / 100 = 0.800$
Ranking from least to greatest steepness: B, C, A.

Q2

The ramp at a loading dock rises 2.5 metres over a run of 4 metres. Find the slope of the ramp.

Answer: Slope = $\frac{\text{Rise}}{\text{Run}} = \frac{2.5}{4} = 0.625$.

Q4

An accessibility ramp for wheelchairs is to be made alongside the staircase. The guidelines given for the slope of the ramp is 1 cm vertical rise to 12 cm horizontal length. What should be the horizontal length of the ramp if the total height of the stairs is 18 cm?

Answer: The required slope is $\frac{\text{Rise}}{\text{Run}} = \frac{1}{12}$.
Given total rise = 18 cm.
$\frac{18}{\text{Run}} = \frac{1}{12} \implies \text{Run} = 18 \times 12 = 216$ cm.
The horizontal length should be 216 cm (or 2.16 metres).