Unit 7 Class 9 Math Solutions Sindh Board

Unit 7 Class 9 Math Solutions Sindh Board are available below for Exercises 7.1 to 7.3 and the Unit 7 Review Exercise. Students can view and download each PDF to study complete step-by-step solutions.

This unit covers ordered pairs, the Cartesian plane, plotting points, graphs of linear equations and practical applications of straight-line graphs. For other units, visit our Class 9 Math Notes Sindh Board page.

Unit 7 Class 9 Math Exercise Solutions

Select an exercise below to view or download its complete PDF solutions.

Unit 7 Quick Overview

Unit 7 Class 9 Math Solutions Sindh Board

What Are Linear Graphs?

A linear graph is the graph of a linear equation in two variables. It forms a straight line on the Cartesian plane.

A common form of a linear equation is:\[ y=mx+c \]

Here, \(m\) represents the slope and \(c\) represents the y-intercept.

For example:\[ y=2x+1 \]

If \(x=0\), then:\[ y=2(0)+1=1 \]

This gives the ordered pair:\[ (0,1) \]

If \(x=1\), then:\[ y=2(1)+1=3 \]

This gives the ordered pair:\[ (1,3) \]

Plotting these points and joining them gives a straight line.

Exercise 7.1 – Ordered Pairs and the Cartesian Plane

Exercise 7.1 introduces ordered pairs, coordinate axes, quadrants and the location of points on the Cartesian plane.

Ordered Pairs

An ordered pair is written in the form:\[ (x,y) \]

The first number gives the horizontal position and the second number gives the vertical position.

For example:\[ (3,2) \]

means moving 3 units along the x-axis and 2 units along the y-axis.

The order matters:\[ (3,2)\neq(2,3) \]

The Cartesian Plane

The Cartesian plane is formed by two perpendicular number lines:

The horizontal line is the x-axis.
The vertical line is the y-axis.
Their point of intersection is the origin.

\[ O=(0,0) \]

Quadrants

Quadrant	Signs
First	\((+,+)\)
Second	\((-,+)\)
Third	\((-,-)\)
Fourth	\((+,-)\)

For example:\[ (4,3) \]

lies in the first quadrant, while:\[ (-4,3) \]

lies in the second quadrant.

Points on the Axes

A point on the x-axis has the form:\[ (a,0) \]

A point on the y-axis has the form:\[ (0,b) \]

Plotting Points

Start from the origin.
Move horizontally according to the x-coordinate.
Move vertically according to the y-coordinate.
Mark and label the point.

Drawing Shapes on a Graph

Several points can be plotted and joined to form geometrical shapes.

For example:\[ A(1,1),\quad B(5,1),\quad C(5,4),\quad D(1,4) \]

These points form a rectangle when joined in order.

Exercise 7.2 – Graphs of Linear Equations

Exercise 7.2 focuses on constructing tables of values and drawing graphs of linear equations in two variables.

Linear Equation in Two Variables

The general form is:\[ ax+by+c=0 \]

For example:\[ x+y=4 \]

Some ordered-pair solutions are:\[ (0,4),\quad(1,3),\quad(2,2),\quad(3,1),\quad(4,0) \]

Constructing a Table of Values

Consider:\[ y=x+2 \]

\(x\)	\(y\)	Ordered Pair
-2	0	\((-2,0)\)
0	2	\((0,2)\)
2	4	\((2,4)\)

Plot the points and join them with a straight line.

Checking a Point

Consider:\[ y=2x+1 \]

Check the point:\[ (2,5) \]

Substitution gives:\[ 5=2(2)+1 \] \[ 5=5 \]

Therefore, the point lies on the graph.

Horizontal Lines

An equation of the form:\[ y=c \]

represents a horizontal line parallel to the x-axis.

Vertical Lines

An equation of the form:\[ x=a \]

represents a vertical line parallel to the y-axis.

Lines Passing Through the Origin

An equation of the form:\[ y=mx \]

passes through the origin.

Slope-Intercept Form

The form:\[ y=mx+c \]

shows the slope \(m\) and y-intercept \(c\).

Exercise 7.3 – Applications of Linear Graphs

Exercise 7.3 uses linear graphs to represent relationships between quantities and solve practical problems.

Conversion Graphs

A conversion graph shows the relationship between two units.

For example:\[ 8\text{ km}=5\text{ miles} \]

Kilometres	Miles
0	0
8	5
16	10
24	15

Temperature Conversion

The relationship between Celsius and Fahrenheit is:\[ F=\frac{9}{5}C+32 \]

For \(C=20\):\[ F=\frac{9}{5}(20)+32=68 \]

Currency Conversion Graphs

If one unit of a foreign currency equals \(r\) Pakistani rupees, then:\[ y=rx \]

Students should use the exchange rate given in the textbook question.

Cost and Quantity Graphs

If one item costs \(p\) rupees and \(x\) items are purchased, then:\[ y=px \]

For example, if one notebook costs 40 rupees:\[ y=40x \]

Graphical Solution of Two Equations

Two linear equations can be solved by drawing both graphs on the same coordinate plane.

For example:\[ x+y=5 \] \[ x-y=1 \]

The lines intersect at:\[ (3,2) \]

Therefore:\[ x=3,\qquad y=2 \]

Possible Relationships Between Two Lines

Intersecting lines give one solution.
Parallel lines give no common solution.
Coincident lines give infinitely many solutions.

Reading Values from a Graph

Locate the known value on one axis.
Move toward the graph.
Move from the graph to the other axis.
Read the corresponding value using the scale.

Unit 7 Review Exercise

Ordered pairs and quadrants
Cartesian plane and coordinate axes
Plotting points
Drawing shapes using coordinates
Linear equations in two variables
Tables of ordered pairs
Horizontal and vertical lines
Graphs in the form \(y=mx+c\)
Conversion graphs
Graphical solution of equations
Practical applications of linear graphs
Multiple-choice and short questions

Important Forms and Rules from Unit 7

\[ ax+by+c=0 \] \[ y=mx+c \] \[ y=c \] \[ x=a \] \[ y=mx \] \[ F=\frac{9}{5}C+32 \]

Common Mistakes to Avoid

Writing the y-coordinate before the x-coordinate
Using incorrect quadrant signs
Choosing an unsuitable scale
Failing to label the axes
Plotting points inaccurately
Drawing a curved line instead of a straight line
Using only one point to draw a line
Making errors in the table of values
Confusing horizontal and vertical lines
Reading values from the wrong axis

How to Prepare Unit 7 for Exams

Learn the signs of coordinates in all four quadrants and practise plotting points accurately.

Choose a suitable scale, label both axes and mark every point clearly.

Prepare a table with at least two or three ordered pairs before drawing a linear graph.

Practise horizontal lines, vertical lines, lines through the origin and conversion graphs.

After attempting each question, use the Unit 7 Class 9 Math Solutions Sindh Board PDFs to check your table, graph and final answer.

Why These Unit 7 Solutions Are Helpful

Explain ordered pairs and quadrants
Show how to plot points correctly
Explain tables of values
Show how to draw straight-line graphs
Cover horizontal and vertical lines
Explain conversion graphs
Help solve equations graphically
Support homework and exam preparation

Frequently Asked Questions

What is the name of Unit 7?

The name of Unit 7 is Linear Graphs and Their Applications.

How many exercises are included?

Unit 7 contains Exercises 7.1, 7.2 and 7.3, followed by a Review Exercise.

What is covered in Exercise 7.1?

Exercise 7.1 covers ordered pairs, quadrants, plotting points and drawing shapes.

What is covered in Exercise 7.2?

Exercise 7.2 covers tables of values and graphs of linear equations.

What is covered in Exercise 7.3?

Exercise 7.3 covers conversion graphs, applications and graphical solutions.

Can students download the PDFs?

Yes. Separate viewable and downloadable PDFs are provided for all exercises and the review exercise.

Related Class 9 Math Resources

Disclaimer

These solutions are prepared for educational support. Students should also consult their official Sindh Textbook Board Mathematics book and follow their teacher’s instructions.

Final Words

The Unit 7 Class 9 Math Solutions Sindh Board provide complete exercise-wise help with ordered pairs, Cartesian coordinates, linear equations, straight-line graphs and their applications.

For solutions to all other units, visit the Class 9 Math Notes Sindh Board page.