# Find the equation of the line passing through ( - 3, 5) and perpendicular to the line through the points (2, 5) and ( - 3, 6).

Given: The line perpendicular to the line passing through (2,5) and ( - 3,6) passes through ( - 3,5).

Formula to be used: If (a,b) and (c,d) are two points then the equation of the line passing through them is

Product of slopes of two perpendicular lines = - 1

The equation of the line joining points (2,5) and ( - 3,6) is

Or, 5y - 25 = - x + 2

i.e. the given line is x + 5y = 27.

The slope of this line is .

the slope of the perpendicular line =

The equation of the line can be written in the form y = 5x + c.

(c is the y - intercept)

This line passes through ( - 3,5).

Hence, 5 = 5x( - 3) + c or, c = 20

The required equation of the line will be y = 5x + 20

i.e. 5x - y + 20 = 0

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