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Mathematics

Grade-8

Easy

Question

Which of the following is the equation of a line that passes through the point (1, 3) and is parallel to the x-axis (i.e., a horizontal line)?

x + 3y = 0
y = 3x
y = 3
x = 1

hint Hint:

1. An equation refers to the relationship between 2 expressions represented with an equal to sign i.e. '='.
2. Equation of a line in slope point form is- (y-y1) = m (x-x1)
3. Parallel lines have equal slopes.
4. Slope of x-axis is 0.

The correct answer is: y = 3

GIVEN-
The given line-
1. Passes through the point (1,3) and
2. Is parallel to x-axis
TO FIND-
Equation of the line.
SOLUTION-
We know that the given line is parallel to x-axis and slopes of parallel lines are equal.
∴ Slope of the given line = m = slope of x-axis
∴ Slope of the given line = m = 0 .......... (Slope of x-axis is 0) .......................... (Equation i)
Also, the given line passes through the point (1,3).
i.e. x1 = 1 & y1 = 3
∴ we use the slope point formula to find the equation of the given line as-
(y-y1) = m (x-x1)
∴ y - 3 = 0 (x - 1) .................................... (From equation i and given information)
∴ y - 3 = 0
∴ y = 3 ............................................... (Adding 3 on both the sides)
Final Answer:-
Option 'c' i.e. 'y = 3' is the correct answer to the given question.

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