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

Hint:

### 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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