Question

# Identify the line having y-intercept =

- y = 2x + 1
- x = 2y +2
- 4y – 8x = 2
- x = 2y

## The correct answer is: 4y – 8x = 2

### Hint:-

Y-intercept for a line is a point at which the given line intersects with the y-axis i.e. the point at which x = 0.

Step-by-step solution:-

The given line has y-intercept = .

y-intercept is the point at which x-coordinate is 0

∴ The given point is (0,)

We substitute (0,1/2) in the given equations to find whether LHS = RHS or not.

a. y = 2x + 1

∴ = 2 (0) + 1

∴ = 0 + 1

∴ 1/2 ≠ 1

∴ LHS ≠ RHS

b. x = 2y +2

∴ 0 = 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 ≠

b. x = 2y + 2

∴ x - 2 = 2y

∴ (x - 2) / 2 = y

∴ x - = y

∴ x - 1 = y

i.e. y = x - 1

Comparing this equation with y = mx + b, we get b = -1 ≠

c. 4y – 8x = 2

∴ 2y - 4x = 1 .................. (Dividing both sides by 2)

∴ 2y = 4x + 1

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

∴ Comparing this equation with y = mx + b, we get b =

d. x = 2y

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

i.e. y = x + 0

Comparing this equation with y = mx + b, we get b = 0 ≠

∴ Option c i.e. 4y - 8x = 2 has y-intercept =

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