Identify the line having y-intercept = 1/2

The correct answer is: 4y – 8x = 2

Step-by-step solution:-
The given line has y-intercept = 1/2.
y-intercept is the point at which x-coordinate is 0
∴ The given point is (0,1/2)
We substitute (0,1/2) in the given equations to find whether LHS = RHS or not.
a. y = 2x + 1
∴ 1/2 = 2 (0) + 1
∴ 1/2 = 0 + 1
∴ 1/2 ≠ 1
∴ LHS ≠ RHS
b. x = 2y +2
∴ 0 = 2 (1/2) + 2
∴ 0 = 1 + 2
∴ 0 ≠ 3
∴ LHS ≠ RHS
c. 4y – 8x = 2
∴ 4 (1/2) - 8 (0) = 2
∴ 2 - 0 = 2
∴ 2 = 2
∴ LHS = RHS
d. x = 2y
∴ 0 = 2 (1/2)
∴ 0 ≠ 1
∴ LHS ≠ RHS
Final Answer:-
∴ Option c i.e. 4y - 8x = 2 is the correct option.
Note:-
Alternatively, we can simplify the given equations and compare it with slope-intercept formula to find the value of y-intercepts-
a. y = 2x + 1
∴ Comparing this equation with y = mx + b, we get b = 1 ≠ 1/2
b. 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 equation with y = mx + b, we get b = -1 ≠ 1/2
c. 4y – 8x = 2
∴ 2y - 4x = 1 .................. (Dividing both sides by 2)
∴ 2y = 4x + 1
∴ y = 2x + 1/2 ...... (Dividing both sides by 2)
∴ Comparing this equation with y = mx + b, we get b = 1/2
d. x = 2y
∴ 1/2 x = y ................. (Dividing both sides by 2)
i.e. y = 1/2 x + 0
Comparing this equation with y = mx + b, we get b = 0 ≠ 1/2
∴ Option c i.e. 4y - 8x = 2 has y-intercept = 1/2