Question
The equation of a line that is perpendicular to the line y = x - 1 and passes through the point (7, 2) is ______.
- y = -x + 9
- y = x - 9
- y = -x - 1
- y = x + 9
Hint:
To write a straight line perpendicular to a given straight line we proceed as follows:
Step I: Interchange the coefficients of x and y in equation ax + by + c = 0.
Step II: Alter the sign between the terms in x and y of equation i.e., If the coefficient of x and y in the given equation are of the same signs make them of opposite signs and if the coefficient of x and y in the given equation are of the opposite signs make them of the same sign.
Step III: Replace the given constant of equation ax + by + c = 0 by an arbitrary constant.
The correct answer is: y = -x + 9
To write a straight line perpendicular to a given straight line we proceed as follows:
Step I: Interchange the coefficients of x and y in equation y = x - 1.
y - x + 1 = 0
x - y + 1 = 0
Step II: Alter the sign between the terms in x and y of equation i.e., If the coefficient of x and y in the given equation are of the same signs make them of opposite signs and if the coefficient of x and y in the given equation are of the opposite signs make them of the same sign.
x + y + 1 = 0
Step III: Replace the given constant of equation ax + by + c = 0 by an arbitrary constant.
x + y + K =0 (1)
Since the line passes through points (7,2), put the values of x and y in equation 1 and find the value of K
7 + 2 + K = 0
K = -9
Substitute the value of K in equation 1
x + y -9 = 0
y = -x + 9
So, the equation of the line ,perpendicular to the line y = x - 1 will be y = -x + 9.
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