Maths-
General
Easy

Question

Identify the line having y-intercept = 1/2

  1. y = 2x + 1
  2.  x = 2y +2
  3. 4y – 8x = 2
  4. x = 2y

hintHint:

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.

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

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