Maths-
General
Easy
Question
Identify the line having slope 2.
- x = 2y + 2
- 2y = x + 2
- 2y = x
- 2y = 4x + 4
The correct answer is: 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
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
∴ 
x - 
= y
∴ x - 1 = y
i.e. y = x - 1
Comparing this with y = mx + c, we get m = ≠ 2
b. 2y = x + 2
∴ y = (x + 2) / 2 .................................... (Dividing both sides by 2)
∴ y = x +
∴ y = x + 1
Comparing this with y = mx + c, we get m = ≠ 2
c. 2y = x
∴ y = x ............................... (Dividing both sides by 2)
∴ y = x + 0
Comparing this with y = mx + c, we get m = ≠ 2
d. 2y = 4x + 4
∴ y = 
x + …......................... (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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