Class 9 Maths Ganita Manjari Chapter 13 Exercise 13.3 Solutions Two Variables, One Line

Class 9 Maths Ganita Manjari Chapter 13 Exercise 13.3 Solutions – Two Variables, One Line help students understand the graphical representation of linear equations in two variables. This exercise focuses on plotting points, drawing straight-line graphs, identifying whether given points lie on a line, and understanding the relationship between an equation and its graph.

The step-by-step solutions make it easier for students to interpret graphs, verify solutions visually, and build a strong foundation for solving pairs of linear equations.

Class 9 Maths Ganita Manjari Chapter 13 Exercise 13.3 Solutions Two Variables, One Line

NCERT Class 9 Maths Ganita Manjari Chapter 13 Exercise Set 13.3

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

Class 9 Maths Ganita Manjari Chapter 13 Exercise Set 13.3 Question 1
Answer:

Steepness can be compared using the slope:

Slope = Rise / Run

For each hill:

  • A: 60/70 = 6/7 ≈ 0.86
  • B: 60/110 = 6/11 ≈ 0.55
  • C: 80/100 = 4/5 = 0.80

Therefore, from least steep to greatest steepness:

B < C < A

So, the order is B, C, A.

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

Answer:

The slope of a ramp is calculated as:

Slope = Rise / Run

Given:

Rise = 2.5 m
Run = 4 m

So,

Slope = 2.5 / 4 = 0.625 = 5/8

Therefore, the slope of the ramp is 5/8 or 0.625.

3. Find the slope of the line l in each of the following diagrams.

Class 9 Maths Ganita Manjari Chapter 13 Exercise Set 13.3 Question 3
Answer:

(i) The line is horizontal.
Rise = 0

Slope = 0

(ii) Using the marked points, the line goes down 1 unit for every 1 unit moved to the right.

Slope = −1

(iii) Taking the marked points (−3, −2) and (2, 2):

Slope = (2 − (−2)) / (2 − (−3)) = 4/5

Slope = 4/5

(iv) The line is vertical, so the run is 0. Division by 0 is not defined.

Slope = Undefined

Therefore, the slopes are:

(i) 0 (ii) −1 (iii) 4/5 (iv) Undefined

4. 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?

Class 9 Maths Ganita Manjari Chapter 13 Exercise Set 13.3 Question 4

Answer:

The ramp guideline is:

1 cm vertical rise : 12 cm horizontal length

Given the total vertical rise is 18 cm:

Horizontal length = 18 × 12 = 216 cm

Therefore, the required horizontal length of the ramp is:

216 cm, or 2.16 m.

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