Class 9 Graph of a Linear Equation — practice questions with answers
Linear Equations · 5 sample questions from the school syllabus. Try each one, then open the answer and the worked solution.
1. The graph of a linear equation in two variables is always a:
Astraight line
Bcircle
Cparabola
Dsingle point
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Answer: A) straight line
Every linear equation in two variables ax + by + c = 0 represents a straight line when plotted on the Cartesian plane.
2. If the point (a, 4) lies on the line y = 2x, find a. (Enter the number.)
A4
B2
C3
D1
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Answer: B) 2
Put y = 4 in y = 2x: 4 = 2a, so a = 2.
3. Riya is plotting the graph of x + y = 8 for a class project. She wants to find the two points where the line cuts the axes. Which pair of points should she plot?
A(8, 0) and (0, 8)
B(0, 8) and (8, 8)
C(8, 0) and (8, 8)
D(4, 4) and (0, 0)
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Answer: A) (8, 0) and (0, 8)
x-axis: y = 0 gives x = 8 -> (8,0). y-axis: x = 0 gives y = 8 -> (0,8). These are the axis-intercepts.
4. A line graph for y = 3x - 2 passes through several points. Which one of the following points does NOT lie on this line?
A(2, 5)
B(1, 1)
C(0, -2)
D(3, 7)
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Answer: A) (2, 5)
y = 3x - 2. At x=2, y = 4, so (2,5) is wrong. Check others: (1,1) 1=1, (0,-2) -2=-2, (3,7) 7=7 all correct.
5. The line 5x + 2y = 20 cuts the axes at points P (on the x-axis) and Q (on the y-axis). O is the origin. Find the area of triangle OPQ (in square units).
A18
B40
C22
D20
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Answer: D) 20
x-intercept: y=0 -> 5x=20 -> x=4, so P(4,0). y-intercept: x=0 -> 2y=20 -> y=10, so Q(0,10). Area = 21(4)(10)=20 sq units.