Maths-
General
Easy

Question

Find a value for k so that the line through (35, k) and (42, 27) is parallel to the line with equation y = x. Application

hintHint:

1. Slopes of parallel lines are equal.
2. When we have 2 points that lie on a given line then we can find the equation of the said line by using the 2-point formula-
(y-y1) = (y2-y1) × (x-x1)
(x2-x1)

The correct answer is: Value of k for the given line is 20.


    Step-by-step solution:-
    y = x
    ∴ y = x + 0.
    Comparing the above equation with standard form of a line i.e. y = mx + c, we get- m = 1 ......................... (Equation i)
    The given line is parallel to y = x
    and we know that parallel lines have equal slopes.
    ∴ Slope of the given line = slope of line (y = x)
    ∴ Slope of the given line = m = 1 ..................... (From Equation i) .................................................................... (Equation ii)
    The given line passes through the point (35,k) & (42,27).
    Hence, x1 = 35, y1 = k, x2 = 42 & y2 = 27
    (y-y1) = (y2-y1) × (x-x1)
    (x2-x1)
    ∴ (y-k) = (27-k) × (x- 35)
    42-35
    ∴ y - k = 27 - k ×(x - 35)
    7
    ∴ 7 * (y - k) = (27 - k) × (x - 35) ............................................................................ (Multiplying both sides by 7)
    ∴ 7y - 7k = 27x - 945 - kx + 35k
    ∴ 7y = 27x - k x + 35k + 7k - 945
    ∴ 7y = (27 - k) x + 42k - 945
    ∴ y = (27 - k)/7 x + 6k - 135 ........................... (Dividing both sides by 7) ........................................... (Equation iii)
    Comparing Equation iii with the standard form of a straight line i.e. y = mx + c, we get-
    m = (27 - k) / 7
    ∴ 1 = (27 - k) / 7 ..................................... (From Equation ii)
    ∴ 7 = 27 - k ...................................... (Multiplying both sides by 7)
    ∴ k = 27 - 7
    ∴ k = 20.

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