Find an equation for the line perpendicular to y x and cont

Find an equation for the line perpendicular to y = x, and contains the point (0, 1). Write your equation in standard form. Remember to show all your work.

Solution

Given equation of line is y= x

compare it with y= mx+b, we have slope m= 1

Now we know the required line is perpendicular to this goven line, hence its slope is negative of reciprocal of the line y= x

Therefore slope of required line = -1

And it passes through (0, 1)

Hence using point slope form of line

y- y1 = m (x-x1)

=> y - 1 = -1(x-0)

=> y -1 = -x

=> x +y -1 =0