Maths-

General

Easy

Question

# Identify the line having slope 2.

- x = 2y + 2

- 2y = x + 2
- 2y = x

- 2y = 4x + 4

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. Equation of a straight line in standard form-

y = mx + c

## The correct answer is: 2y = 4x + 4

### Step-by-step solution:-

We will simplify the given equations and compare the same with standard form of a straight line to find the value of m.

a. x = 2y + 2

∴ x - 2 = 2y

∴ (x - 2) / 2 = y

∴ 1/2 x - 2/2 = y

∴ 1/2 x - 1 = y

i.e. y = 1/2 x - 1

Comparing this with y = mx + c, we get m = 1/2 ≠ 2

b. 2y = x + 2

∴ y = (x + 2) / 2 .................................... (Dividing both sides by 2)

∴ y = 1/2 x + 2/2

∴ y = 1/2 x + 1

Comparing this with y = mx + c, we get m = 1/2 ≠ 2

c. 2y = x

∴ y = 1/2 x ............................... (Dividing both sides by 2)

∴ y = 1/2 x + 0

Comparing this with y = mx + c, we get m = 1/2 ≠ 2

d. 2y = 4x + 4

∴ y = 4/2 x + 4/2 …......................... (Dividing both sides by 2)

∴ y = 2x + 2

Comparing this with y = mx + c, we get m = 2

Final Answer:-

∴ Option d i.e. 2y = 4x + 4 is the correct option because its slope = m = 2.

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