Helppp

what is the equation of the line that passes through the point of intersection of the lines

y=2x-4 and y=-x+2, and is also parallel to the line y=1/2x+4?

Let's find the point where the first two lines intersect....setting the y's equal, we have :

2x - 4  = -x + 2    add x, 4 to both sides

3x  = 6       divide by 3  on both sides

x = 2       so using this value in  y = -x + 2.......y = 0

So....the intersection point of the first two lines = (2, 0 )

And parallel lines have the same slope....so....the slope of our line = 1/2......and we have

y  - 0   = (1/2)(x - 2)

y = (1/2)x - 1       and that's the equation of our line