Write an equation of the line that passes through (-4,1) and is perpendicular to the line y = 2x + 3.

line1:y=2x+3

Gradient1=2

Let line2 be the line passes through (-4,1)and perpendicular to line1.

Because line2 and line1 are perpendicular, (gradient of line2) (gradient of line1) =-1

Gradient of line2=-1/2

Equation of line2:y-y1 =m(x-x1)

:y-1 =(-1/2)[x-(-4)]

:(y-1)(-2)=(x+4)

:-2y+2 =x+4

:-2y+2-x-4=0

:-x-2y-2 =0

:x+2y+2 =0

*notes:gradient=m

set each factor equal to 0

4x-3 = 0

2x-1 = 0

solve for x.

4x-3=0

4x=3

x= 3/4

solve for x. 

2x-1= 0

2x= 1

x= 1/2

eventually after a few more steps, your answer should be 1/2 is less than or equal to x and 3/4 is greater than or equal to x