Mathematics
Assertion (A): A line is parallel to the line 2x – 3y = 7 and it passes through the point (0, 4). The equation of this line is 2x – 3y – 12 = 0.
Reason (R): If two lines are parallel, then sum of their slopes is equal to 1.
A is true, R is false
A is false, R is true
Both A and R are true
Both A and R are false
Straight Line Eq
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Answer
A line is parallel to 2x − 3y = 7 and passes through (0, 4).
⇒ 2x - 3y = 7
⇒ -3y = -2x + 7
⇒ y =
Comparing above equation with y = mx + c, we get: m =
Since the lines are parallel, the slope of parallel line = .
The required line passes through (0, 4), so its y-intercept is c = 4.
Using the slope-intercept form y = mx + c:
⇒ y = x + 4
⇒ 3y = 2x + 12
⇒ 2x - 3y + 12 = 0
Assertion (A) is False.
The condition for two lines to be parallel is that their slopes are equal m1 = m2.
Reason (R) is False.
Hence, option 4 is the correct option.
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