Maths-
General
Easy
Question
Identify the equation of a line parallel to the line y = x – 1
- y = 2x - 1
- x = y - 1
- x + y = 1
- y = x + 1
The correct answer is: x = y - 1
Hint:-
1. The slope of a line can be defined as the change in y coordinates of any 2 points on that line corresponding to the change in the x coordinates of those 2 points. This is generally referred to as the rise to run ratio of the given line i.e. how much did the y-coordinates rise vis-a-vis how long a distance was covered by the x-coordinates. Slope = m = rise / run = y2-y1 / x2-x1
2. Slopes of paralle lines are equal.
Step-by-step solution:-
y = x - 1
Comparing the above equation with standard form of a line i.e. y = mx + c, we get-
m = 1 …...................................................................... (Equation i)
Now, we know that slopes of parallel lines are equal.
∴ Slope of line parallel to the given line = slope of given line
∴ Slope of line perpendicular to the given line = 1
∴ We need to find the line from the given options, whose slope = 1.
a. y = 2x - 1
Comparing the above equation with standard form of a line i.e. y = mx + c, we get-
m = 2 ≠ 1
b. x = y - 1
∴ x + 1 = y
i.e. y = x + 1
Comparing the above equation with standard form of a line i.e. y = mx + c, we get-
m = 1
c. x + y = 1
∴ y = -x + 1
Comparing the above equation with standard form of a line i.e. y = mx + c, we get-
m = -1 ≠ 1
d. y = x + 1
Comparing the above equation with standard form of a line i.e. y = mx + c, we get-
m = 1
Final Answer:-
∴ Option b i.e. x = y - 1 & d i.e. y = x + 1 are both the correct options as both the equations are actually the same.
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