Intercepts of a straight line: Class 9 practice

What you should know first

• Solving linear equations

The idea behind intercepts of a straight line

The x-intercept is where y = 0 and the y-intercept is where x = 0. Two intercepts are enough to draw the line; the area of the triangle it makes with the axes is ½ × |x-int| × |y-int|.

Step-by-step method

1. Set y = 0 to find the x-intercept.
2. Set x = 0 to find the y-intercept.
3. Plot both and join; use them for area.

Worked example 1 (Basic)

Find the intercepts of 4x − 6y = -28.

1. y = 0 → x = -7
2. x = 0 → y = 14/3
3. Answer: x-intercept -7, y-intercept 14/3

Worked example 2 (Standard)

Find the intercepts of 6x − 5y = 6.

1. y = 0 → x = 1
2. x = 0 → y = -6/5
3. Answer: x-intercept 1, y-intercept -6/5

Worked example 3 (Challenge)

Find the area of the triangle formed by 5x + 4y = -10 with the axes.

1. x-intercept -2, y-intercept -5/2
2. Area = ½ × 2 × 5/2 = 5/2
3. Answer: 5/2

Common mistakes and misconceptions

• Mixing up the intercepts
• Forgetting absolute values for area

Practice questions

1. (Basic) Find the intercepts of 2x − 1y = -12.
2. (Basic) Find the intercepts of 1x + 6y = -4.
3. (Standard) Find the intercepts of 1x + 3y = -9.
4. (Standard) Find the intercepts of 3x + 4y = 15.
5. (Challenge) Find the area of the triangle formed by 3x − 1y = -18 with the axes.
6. (Challenge) Find the area of the triangle formed by 4x + 1y = -32 with the axes.

Answer key with full working

• Q1: y = 0 → x = -6 → x = 0 → y = 12 → Answer: x-intercept -6, y-intercept 12
• Q2: y = 0 → x = -4 → x = 0 → y = -2/3 → Answer: x-intercept -4, y-intercept -2/3
• Q3: y = 0 → x = -9 → x = 0 → y = -3 → Answer: x-intercept -9, y-intercept -3
• Q4: y = 0 → x = 5 → x = 0 → y = 15/4 → Answer: x-intercept 5, y-intercept 15/4
• Q5: x-intercept -6, y-intercept 18 → Area = ½ × 6 × 18 = 54 → Answer: 54
• Q6: x-intercept -8, y-intercept -32 → Area = ½ × 8 × 32 = 128 → Answer: 128

Syllabus note

This skill is listed under "Linear Equations in Two Variables" for Class 9 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

• Linear Equations in Two Variables chapter notes (Class 9)
• Solutions of ax + by = c
• Remainder theorem and factor theorem
• Area of a triangle by Heron's formula
• Rationalising the denominator
• Recurring decimals to fractions
• All Class 9 practice

Frequently asked questions

Which chapter is intercepts of a straight line in?

"Linear Equations in Two Variables", Class 9 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.