The equation of the line that goes through the point 95 and

The equation of the line that goes through the point (9,5) and is perpendicular to the line 4x+4y=3 can be written in the form y=mx+b where m is ______and where b is ______

Solution

Given

a line passes through (9,5) and perpendicular to the line 4x +4y = 3

we can rewrite 4x+4y =3 in y=mx + b form

4x +4y =3

subtract 4x from both sides

4x +4y -4x = 3-4x

4y = -4x +3

y = - x +3/4                 // divided both sides by \"4\"

now we compare y=mx+ b

we get m(slope) = -1 and b = 3/4

since this line is perpendicular to the line passes through (9,5)

product of two perpendicular lines = -1

m1 * m2 = -1

-1 * m2 = -1

m2 = 1

now we have slope m = 1 and passes through (9,5)

using point slope form

(y-y1) = m(x-x1)

y-5 = 1(x-9)

y-5 = x-9

now we rearrange this in y=mx+b form

y - 5 = x - 9

y = x -9 +5

y = x - 4

m =1 and b= -4