Find the equation of the line whose y - intercept is - 3 and which is perpendicular to the line joining the points ( - 2, 3) and (4, - 5).

Given: The line perpendicular to the line passing through ( - 2,3) and (4, - 5) has the y - intercept of - 3.

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 ( - 2,3) and (4, - 5) is

or,3y + 15 = - 4x + 16 or, 4x + 3y = 1

Slope of this line is .

the slope of the perpendicular line =

The equation of the line can be written in the form

(c is the y - intercept)

But, the y - intercept is - 3.

The required line is

i.e. 3x - 4y = 12