Mathematics
Assertion (A): The equation of the line whose inclination is 45° and which intersects the y-axis at the point (0, –4) is x – y = 4.
Reason (R): The equation of the line having slope m and y-intercept c is given by y = cx + m.
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
The slope is m = tan θ
m = tan 45° = 1
The line intersects the y-axis at (0, -4), so the y-intercept is c = -4.
By Slope-intercept form,
Equation of line :
⇒ y = mx + c
⇒ y = 1x + (-4)
⇒ y = x - 4
⇒ x - y = 4
Assertion (A) is True.
The correct slope-intercept form is y = mx + c, where m is the slope (gradient) and c is the y-intercept.
Reason (R) is False.
A is true, R is false.
Hence, option 1 is the correct option.
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