Answer:
Slope of the line is -1/4 and y intercept is 2.
Step-by-step explanation:
Let the equation of the required line be given as [tex]\[y=mx+c\][/tex]
The required line is perpendicular to the line [tex]\[y=4x+4\][/tex]
Slope of the line [tex]\[y=4x+4\][/tex] is 4.
[tex]\[=> m*4 = -1\][/tex]
[tex]\[=> m = \frac{-1}{4}\][/tex]
So the equation of the line becomes:
[tex]\[y=\frac{-1}{4}x+c\][/tex]
But this line passes through the point (0,2).
[tex]\[=>2=\frac{-1}{4}*0+c\][/tex]
[tex]\[=>c=2\][/tex]
So the equation of the line is :
[tex]\[y=\frac{-1}{4}x+2\][/tex]
Its slope is -1/4 and y intercept is 2.