Linear graphs: Class 8 practice
A linear graph is a straight line. Read the method, follow the three worked examples, then try the six questions.
What you should know first
- Coordinates
The idea behind linear graphs
A linear graph is a straight line. For y = mx + c, each step of 1 in x changes y by m. Read values from a graph or a table and use the pattern to predict others.
Step-by-step method
- Make a table of x and y.
- Check the change in y per unit x is constant.
- Use it to find the missing value.
Worked example 1 (Basic)
The points (0, -6), (1, -7), (2, -8), (3, -9) lie on a line. Find y when x = 8.
- y changes by -1 for each 1 in x
- y = -1x − 6
- x = 8 → y = -14
- Answer: -14
Worked example 2 (Standard)
The points (0, -10), (1, -1), (2, 8), (3, 17) lie on a line. Find y when x = 14.
- y changes by 9 for each 1 in x
- y = 9x − 10
- x = 14 → y = 116
- Answer: 116
Worked example 3 (Challenge)
A taxi charges ₹34 fixed plus ₹9 per km. Find the fare for 6 km and write the rule.
- Fare = 34 + 9x
- x = 6: ₹88
- Answer: ₹88
Common mistakes and misconceptions
- Reading x and y the wrong way
- Assuming a line passes through the origin
Practice questions
- (Basic) The points (0, -8), (1, -4), (2, 0), (3, 4) lie on a line. Find y when x = 10.
- (Basic) The points (0, 14), (1, 23), (2, 32), (3, 41) lie on a line. Find y when x = 8.
- (Standard) The points (0, -10), (1, -18), (2, -26), (3, -34) lie on a line. Find y when x = 15.
- (Standard) The points (0, 18), (1, 26), (2, 34), (3, 42) lie on a line. Find y when x = 6.
- (Challenge) A taxi charges ₹28 fixed plus ₹6 per km. Find the fare for 8 km and write the rule.
- (Challenge) A taxi charges ₹38 fixed plus ₹7 per km. Find the fare for 14 km and write the rule.
Answer key with full working
- Q1: y changes by 4 for each 1 in x → y = 4x − 8 → x = 10 → y = 32 → Answer: 32
- Q2: y changes by 9 for each 1 in x → y = 9x + 14 → x = 8 → y = 86 → Answer: 86
- Q3: y changes by -8 for each 1 in x → y = -8x − 10 → x = 15 → y = -130 → Answer: -130
- Q4: y changes by 8 for each 1 in x → y = 8x + 18 → x = 6 → y = 66 → Answer: 66
- Q5: Fare = 28 + 6x → x = 8: ₹76 → Answer: ₹76
- Q6: Fare = 38 + 7x → x = 14: ₹136 → Answer: ₹136
Syllabus note
This skill is listed under "Introduction to Graphs" for Class 8 in the NCERT/CBSE books. ICSE, IGCSE, IB and state boards may teach it in a different chapter or year.
Answers on this page are generated and automatically re-checked by a second, independent calculation. They have not been reviewed by a teacher — if you spot a problem, tell us on WhatsApp.
Related practice and notes
Frequently asked questions
Which chapter is linear graphs in?
"Introduction to Graphs", Class 8 Maths (NCERT/CBSE). Other boards may place it differently.
How were the answers checked?
Answers on this page are generated and automatically re-checked by a second, independent calculation. They have not been reviewed by a teacher — if you spot a problem, tell us on WhatsApp.