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What is the equation of the straight line which is perpendicular to y = x and passes throng (3, 2)?

What is the equation of the straight line which is perpendicular to y = x and passes throng (3, 2)? Correct Answer x + y = 5

Concept:

If L1 and L2 are two lines with slope m1 and m2 respectively such that m1 × m2 = - 1. Then the given lines are perpendicular to each other.

The equation of a line passing through the point (x1, y1) and having the slope ‘m’ is y – y1 = m (x – x1).

Calculation:

Given: Point (3, 2) and perpendicular to y = x.

So, by comparing the equation y = x with y = m1x + c, we get m1 (say) = 1.

As we know that, if two lines L1 and L2 are perpendicular to each other with slope m1 and m2 respectively, then m1 × m2 = -1.

So, let the slope of line perpendicular to y = x be m2

⇒ m1 × m2 = 1 × m2 = -1 ⇒ m2 = -1.

So, the equation of line with slope m2 and passing through point (3, 2) is given by

⇒ y – 2 = - 1 × (x - 3) ⇒ x + y = 5.

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