Questions on Graph of Linear Equation for SSC CGL Exam

If you’re preparing for the SSC CGL or any other competitive exam, mastering the topic of Graph of Linear Equations is important. This topic belongs to the Quantitative Aptitude and Data Interpretation sections. If we talk about the SSC CGL Tier 1 exam, then you can expect at least 1-3 questions from the easy to moderate level in the exam. This blog has provided a detailed concept, tips and tricks, and questions on the graph of linear equations for SSC CGL. Along with that, we have provided a free mock test that you can attempt for free so that you can check your exam preparation level.

Graph of Linear Equations: Introduction, Basic Concepts, and Types

Linear equations are algebraic equations of the form ax + by = c, where a, b, and c are constants. The graph of a linear equation in two variables is always a straight line.

Above, we have provided the basic concept about the graph of a linear equation. Below, we have provided the basic characteristics of a linear graph.

Key Characteristics of a Linear Graph

• The graph is always a straight line.
• It may pass through the origin (0,0) if there is no constant term.
• The slope or gradient of the line determines its steepness and direction.
• The y-intercept is the point where the line crosses the y-axis.

Types of Graphs in SSC CGL Questions

Here are the common types of linear graph-related problems you may encounter in SSC exams:

Type 1: Finding Slope and Intercept

Concept:
For an equation of the form y = mx + c:

• m is the slope (rise over run)
• c is the y-intercept

Example Question:
Find the slope and y-intercept of the equation 2x + 3y = 6.

Approach:
Rearrange to slope-intercept form:
→ 3y = -2x + 6
→ y = (-2/3)x + 2

Answer:
Slope = -2/3, Intercept = 2

Type 2: Plotting the Line on Graph

Concept:
Choose values of x, find corresponding y, and plot points to draw the line.

Example Question:
Plot the line represented by the equation x + y = 4.

Approach:

• When x = 0, y = 4 → (0,4)
• When x = 4, y = 0 → (4,0)

Plot these two points and draw a straight line through them.

Type 3: Intersection of Two Lines

Concept:
Two linear equations intersect at a point (x, y), which is the solution to the system of equations.

Example Question:
Find the point of intersection of lines x + y = 5 and x – y = 1

Solution:
Solve using substitution or elimination:
Adding both:
2x = 6 → x = 3
Then y = 5 – 3 = 2

Answer: (3, 2)

Type 4: Parallel and Perpendicular Lines

Concept:

• Lines with the same slope are parallel.
• Lines with negative reciprocal slopes are perpendicular.

Example Question:
Which of the following is perpendicular to the line y = 2x + 3?

Answer:
A line with slope = -1/2 → y = (-1/2)x + c

Key Table for Quick Reference

Graph of Linear Equation Questions for SSC CGL

Here, we have provided the questions on the graph of linear equations for SSC CGL exam preparation. You are strongly advised that if you do not know about the basics of graphs, then first go through that and understand it, and then try to solve these questions by yourself. A PDF is provided with detailed solutions. So, after solving these questions, you can check your answers and understand their solutions if you made any mistakes.

Question 1: A line 3y = 8x- 24 cuts X-axis and Y-axis at points A and B, respectively. Find the distance of the mid-point of AB from a point (3,4).

A) 1.5 units

B) 1 unit

C) 2.5 units

D) 3 units

Question 2: Two lines A and B are perpendicular to each other, line A passes through the point (4,0) and line B passes through the point (0,6). If line A has slope of ‘m’ then find x-coordinate of the point where the two lines meet.

A) 

B) 

C) 

D) 

Question 3: The line passing through the origin and the point of intersection of 3y = x + 3 and 7x + 2y = 14 also passes through the point(s).

A)

B)

C)

D)

Question 4: Find the area in the first quadrant between the lines 3x + 4y = 24 and 4x + 3y = 12.

A) 18 sq. units

B) 24 sq. units

C) 12 sq. units

D) None of the above

Question 5: The co-ordinates of the vertices of a triangle ABC are A (0, 2), B (5, 14) and C (20, 14). Find the ratio of AB: BC.

A) 21:37

B) 10:23

C) 13:15

D) 32:25

Question 6: Find the area of a triangle whose vertices are (-5, -1), (3, -5) and (5, 2).

A) 32 square units

B) 22 square units

C) 26 square units

D) 64 square units

Question 7: Find the intersection point of the medians of a triangle formed by the point A(1,4), B(4,2) and C(-2,1).

A) (1, 2)

B) 

C)

D)

Question 8: Find the area of the triangle enclosed by the line 2x + 5y = 10, x = 0 and y = 0 in the first quadrant.

A) 10 sq. units

B) 5 sq. units

C) 7.5 sq. units

D) None of these

Question 9: Find the line passing through the point (3, 6) and parallel to the line through the origin and point of intersection of 3x + y = 5 and x + 2y = 4.

A) 6y = 7x + 15

B) 6y = 3x + 27

C) 3y = 6x

D) 3y = 5x + 3

Question 10: If the points P(2, 3), Q(5, a) and R(6, 7) are co-linear, then find the value of ‘a’.

A) 6

B) 9

C) 4

D) -6

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FAQs: Graph of Linear Equation for SSC CGL

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