What is the equation of the line that passes through the point of intersection of the lines y = 2x − 5 and y = −x + 7, and is also parallel to the line y=1/2x+4?y= -1/2x - 3y= 1/2x+1y= -1/2x + 4y = 2x − 1

FIRST
Find the intersection of the lines y = 2x - 5 and y = -x + 7 by subtitution of y from the two equations.
Find the x-coordinate of the intersection
2x - 5 = -x + 7
2x + x = 7 + 5
3x = 12
x = 4

Find the y-coordinate of the intersection
y = -x + 7
y = -4 + 7
y = 3

The intersection is (4,3)

SECOND
Find the slope of the line
The slope of line y = (1/2)x + 4 is (1/2)
Because the line we need to find is parallel to this line, the slope is the same to the parallel line.
m = 1/2

THIRD
Make the equation by this formula
y - y₁ = m(x - x₁)

From the first part and second part, we know that
(x₁, y₁) = (4,3)
m = 1/2
Input these numbers to the formula

y - y₁ = m(x - x₁)
y - 3 = 1/2 (x - 4)
y - 3 = (1/2)x - 2
y = (1/2)x - 2 + 3
y = (1/2)x + 1

The answer is the second option