Write the equation in slope intercept form for the line perpendicular to c(-4,-5) and d(4,9) passing through the midpoint of the line

Slope intercept form of line passing through midpoint of CD and perpendicular to CD is

Need to find the slope intercept form for the line perpendicular to C(-4,-5) and D(4,9)

And passing through the midpoints of the line CD.

Lets first calculate slope of CD  

Let say slope of CD be represented by

General formula of slope of line passing through points is as follows:

Let’s say slope of required line which is perpendicular to CD be

As product of slope of the lines perpendicular to each other is -1

=> slope of line CD slope of line perpendicular to CD = -1

Now let’s find midpoint of CD

And midpoint of CD will be as follows

So midpoint of CD is ( 0 , 2 )

As it is given that line whose slope intercept form is required is perpendicular to CD and passing through midpoint of CD , we need equation of line passing through ( 0 , 2 ) and having slope as

Generic equation of line passing through and having slope of m is given by

Substituting the values in generic equation of line we get

As we required final equation in slope intercept form which is y = mx + c, lets rearrange our equation is required form:

Hence can conclude that slope intercept form of line passing through midpoint of CD and perpendicular to CD is

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