Respuesta :

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.

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