IGKO is TODAY!
Mock Test ₹150 View Schedule

Ganita Manjari · Class 9 · Part II · Chapter 13

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

Four questions on slope as rise over run: ranking steepness, a loading ramp, reading slopes from graphs, and the length of a wheelchair ramp.

Last updated 6 October 2026

  • 4Questions
  • 0Diagrams
  • Ch 13Two Variables, One Line

How to answer every question

slope = riserun = y2 − y1x2 − x1
  1. Find the rise The vertical change between two points.
  2. Find the run The horizontal change between the same two points.
  3. Divide slope = rise over run.
  4. Check the direction Upward to the right is positive, downward is negative.

Slope: the steepness of a line, rise over run.

Rise: y₂ − y₁, the vertical change.

Run: x₂ − x₁, the horizontal change.

Slope

Chapter 13 Exercise 13.3 Question 1 Solution Rank the ski hills A, B, C from least steep to steepest.

Answer: B, C, A
The hills
Three right-angled triangles drawn as ski hills. Hill A has height 60 m and base 70 m, hill B has height 60 m and base 110 m, hill C has height 80 m and base 100 m.
Q1 · three ski hills (from the book)
Steepness is the slope, rise over run

The steeper the hill, the larger the ratio of the vertical rise to the horizontal run.

HillRiseRunSlope = rise over runAs a decimal
A60 m70 m6070 = 670.857
B60 m110 m60110 = 6110.545
C80 m100 m80100 = 450.8

Compare the fractions without decimals: 67 = 0.857, 45 = 0.8, 611 = 0.545.

From least to greatest steepness: B, C, A (slopes 611, 45, 67).

Chapter 13 Exercise 13.3 Question 2 Solution The ramp at a loading dock rises 2.5 m over a run of 4 m. Find its slope.

Answer: 5/8
The ramp
A loading-dock ramp with a vertical rise marked 2.5 m and a horizontal run marked 4 m.
Q2 · rise 2.5 m, run 4 m (from the book)
Rise over run
slope = riserun = 2.54 = 58 = 0.625

The slope of the ramp is 58 (0.625).

Chapter 13 Exercise 13.3 Question 3 Solution Find the slope of the line l in each of the four diagrams.

Answer: 0, −1, 2/3, undefined
The diagrams
Two grid diagrams. In (i) the line l is horizontal. In (ii) the line l goes down from the upper left to the lower right through the origin.
Q3 (i) and (ii) (from the book)
Two grid diagrams. In (iii) the line l goes up from the lower left to the upper right through two marked points. In (iv) the line l is vertical.
Q3 (iii) and (iv) (from the book)
Reading each slope
DiagramWhat we seeSlope
(i)l is horizontal: y stays the same, so the rise is 002 = 0 (any non-zero run)
(ii)Through the origin and the marked point 2 squares left and 2 squares up: going 2 right, the line goes 2 down−22 = −1
(iii)The marked points are 3 squares apart horizontally and 2 squares apart vertically23
(iv)l is vertical: the run is 0 and we cannot divide by 0undefined

In (ii) and (iii) the squares used are the large grid squares. Any two points on the line give the same slope.

(i) 0, (ii) −1, (iii) 23, (iv) undefined (vertical line).

Chapter 13 Exercise 13.3 Question 4 Solution A ramp for wheelchairs must have 1 cm of vertical rise for every 12 cm of horizontal length. What horizontal length is needed if the stairs are 18 cm high in total?

Answer: 216 cm
The ramp
A wheelchair ramp built alongside a staircase.
Q4 · a wheelchair ramp beside the stairs (from the book)
Use the slope

The slope is 112. Let the horizontal length be L cm. The rise is 18 cm, so:

18L = 112, so L = 18 × 12 = 216

The ramp needs a horizontal length of 216 cm (2.16 m).

Answers at a glance

Slope is always rise over run.

QuestionWhat is askedKey ideaAnswer
Q1 Steepness of ski hillsSlope = rise over runB, C, A
Q2 Slope of a ramp2.5 over 45/8
Q3 Slope from graphsRise over run0, −1, 2/3, undefined
Q4 Ramp length1 over 12 = 18 over L216 cm

Other chapters of Ganita Manjari (Class 9)

Source of the questions: NCERT, Ganita Manjari, Grade 9, Part II, Chapter 13, Exercise Set 13.3. The solutions, explanations and diagrams on this page are our own working.

Call WhatsApp Book Demo