Class 9 Maths – Linear Equations In Two Variables MCQ

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1. The general form of a linear equation in two variables is:

a) ax + by + c = 0
b) ax + by = c
c) ax^2 + by^2 = c
d) ax – by = 0

Answer:

a) ax + by + c = 0

Explanation:

A linear equation in two variables is represented as ax + by + c = 0 where a and b are not simultaneously zero.

2. For the equation 2x + 3y = 6, x-intercept is:

a) 3
b) 2
c) 0
d) 6

Answer:

b) 2

Explanation:

For the x-intercept, y = 0. Plugging this into the equation gives x = 3.

3. For the equation 3x – 4y = 12, y-intercept is:

a) -3
b) 4
c) 3
d) -4

Answer:

a) -3

Explanation:

For the y-intercept, x = 0. Substituting this value gives y = -3.

4. A solution of the equation 2x + y = 7 is:

a) (0, 7)
b) (3.5, 0)
c) (7, 0)
d) (2, 3)

Answer:

a) (0, 7)

Explanation:

Substituting x=0, we get y=7.

5. How many solutions does a linear equation in two variables have?

a) 0
b) 1
c) 2
d) Infinite

Answer:

d) Infinite

Explanation:

A linear equation in two variables represents a straight line, and every point on the line is a solution.

6. The graph of 3x + y = 5 will be a:

a) Parabola
b) Circle
c) Straight Line
d) Ellipse

Answer:

c) Straight Line

Explanation:

Equations in two variables of degree 1 always represent a straight line.

7. If a line intersects x-axis at (a, 0) and y-axis at (0, b), then its equation is:

a) x/a + y/b = 1
b) ax + by = 1
c) x – a + y – b = 0
d) a/x + b/y = 0

Answer:

a) x/a + y/b = 1

Explanation:

Using the intercept form of a line.

8. Which of the following is NOT a linear equation in two variables?

a) 3x + 4y = 12
b) x^2 + y = 7
c) y = 2x + 5
d) 5x – 7y = 0

Answer:

b) x^2 + y = 7

Explanation:

The equation has a term of degree 2.

9. If (2, 3) is a solution of the linear equation in two variables ax + by = c, then:

a) 2a + 3b = c
b) a + 2b = c
c) 3a + 2b = c
d) a + b = c

Answer:

a) 2a + 3b = c

Explanation:

By substituting the given values of x and y.

10. Two parallel lines have:

a) The same slope and different intercepts
b) Different slopes and different intercepts
c) The same slope and same intercepts
d) Different slopes and the same intercept

Answer:

a) The same slope and different intercepts

Explanation:

Parallel lines have equal slopes but different y-intercepts.

11. The graph of x = 3 is:

a) A line parallel to x-axis
b) A line parallel to y-axis
c) A line passing through the origin
d) A circle of radius 3

Answer:

b) A line parallel to y-axis

Explanation:

x=3 represents a vertical line at x=3 on the graph.

12. The equation of a line passing through the origin is of the form:

a) y = mx
b) y = mx + c
c) ax + by = c
d) ax + by + c = 0

Answer:

a) y = mx

Explanation:

Lines passing through the origin have the form y = mx where m is the slope.

13. If two lines are perpendicular, the product of their slopes is:

a) 0
b) 1
c) -1
d) Undefined

Answer:

c) -1

Explanation:

The product of the slopes of two perpendicular lines is always -1.

14. The equation representing a line parallel to x-axis and at a distance of 4 units below it is:

a) y = -4
b) x = -4
c) y = 4
d) x = 4

Answer:

a) y = -4

Explanation:

This line will be parallel to the x-axis and will pass through y=-4.

15. A line with zero slope is:

a) Vertical
b) Horizontal
c) Slanting to the right
d) Slanting to the left

Answer:

b) Horizontal

Explanation:

A horizontal line has a slope of 0.

16. The slope of the line 2x – 3y = 6 is:

a) 2/3
b) -3/2
c) 3/2
d) -2/3

Answer:

c) 3/2

Explanation:

Rearranging the equation to the form y = mx + c, we get the slope m = 3/2.

17. Which of the following equations represents a line with undefined slope?

a) y = 2x + 3
b) x = 5
c) y = 7
d) 2x + 3y = 6

Answer:

b) x = 5

Explanation:

The equation x=5 represents a vertical line, which has an undefined slope.

18. The slope of the line passing through the points (1,2) and (3,6) is:

a) 2
b) 3
c) 1/2
d) 4

Answer:

a) 2

Explanation:

Using the slope formula, (y2-y1)/(x2-x1) = (6-2)/(3-1) = 2.

19. For the equation y = mx, the y-intercept is:

a) m
b) 0
c) 1
d) x

Answer:

b) 0

Explanation:

The line passes through the origin, so y-intercept is 0.

20. Which of the following is the equation of the y-axis?

a) x = 0
b) y = 0
c) y = x
d) x = y

Answer:

a) x = 0

Explanation:

All points on the y-axis have x-coordinate as 0.

Related MCQ (Multiple Choice Questions) :

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