Class 9 Lines Parallel to the Axes — 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 the equation x = 4 is a line that is:
Aparallel to the y-axis
Bparallel to the x-axis
Cpassing through the origin
Dthe x-axis itself
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Answer: A) parallel to the y-axis
An equation of the form x = a (a constant) gives a vertical line, which is parallel to the y-axis (4 units to its right).
2. The point where the line x = 6 cuts the x-axis is:
A(6, 0)
B(0, 6)
C(6, 6)
D(0, 0)
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Answer: A) (6, 0)
On the x-axis y = 0. Combined with x = 6 gives the intersection point (6, 0).
3. Which statement about the line y = b (b not equal to 0) is FALSE?
AIt passes through the origin
BIt is parallel to the x-axis
CEvery point on it has y-coordinate b
DIt meets the y-axis at (0, b)
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Answer: A) It passes through the origin
Since b is not 0, the line y = b never passes through (0, 0). The other three statements are all true.
4. The lines x = -2, x = 6 and y = 1 bound three sides of a square that opens upward. The fourth side is a horizontal line forming the top. If the square's side length equals the gap between the vertical lines, what is the equation of the top side?
Ay = 9
By = 7
Cy = 8
Dy = 6
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Answer: A) y = 9
Gap between vertical lines = |6 - (-2)| = 8, the side length. The base is y = 1; the top is 8 units higher: y = 1 + 8 = 9.
5. A rectangular tile on a design grid is bounded by x = 2, x = 2 + w, y = -1 and y = 5. Its diagonal length is 10 units. Find the width w of the tile (w > 0).
A9
B16
C7
D8
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Answer: D) 8
Height = |5 - (-1)| = 6. For a rectangle, diagonal² = width² + height²: 10² = w² + 6², so 100 = w² + 36, w² = 64, w = 8.