Help please Geometry urgent

Question

Which equation in slope-intercept form represents a line that is parallel to y=1/2x-2 and passes through the point (-8,1)

a) y= 1/2x-9

b) y= 1/2x+5

c) -1/2x+5

Answer 1

The line parallel to this one will have the same slope. In the equation provided, the slope, m=1/2. Then you can use the following equation. (y-y1)=m(x-x1)

Plug in the values of (x1,y1) using the point provided. (-8,1)

(y-1)=1/2(x-(-8)) Simplify

(y-1)=1/2(x+8) Distribute

y-1=1/2x+4 Add 1 to both sides

y-1+1=1/2x+4+1 Simplify

y=1/2x+5 or b)

Answer 2

The answer is b) y=1/2x + 5

Since two lines are parallel, then they have the same slope (1/2),

then, y = 1/2 x + b

the line passes through point (-8,1), means 1=1/2 (-8) + b, solving b, then

the y-intercept b = 5

Therefore the equation is: y=1/2 x + 5