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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length 10 m. If the seating portion of the hall has an area of 180 square meters, what is the value of *x *?

**Note:**

There are different concepts used to solve this problem. Another concept used which is not mentioned in the hint is that the perpendicular drawn from the vertex of an isosceles triangle to the

base cuts the base in half. This property is also applicable in equilateral triangles as they are a special case of isosceles triangle.