The equation of line ef is y = 1/2x + 6. write an equation of a line parallel to line ef in slope-intercept form that contains point (0, −2).

y = −2x − 2
y = -1/2x + 2
y = 1/2x − 2
y = − 2x + 2

The answer is y = 1/2x - 2

y = mx + b
m - the slope
b - y-intercept

Line EF is y = 1/2x + 6. Its slope is: m = 1/2. Parallel line will have the same slope.

Parallel line:
y = 1/2x + b

Calculate b by substituting contains point (0, −2):
-2 = 1/2 * 0 + b
-2 = 0 + b
-2 = b

Now when we have both m and b, the parallel line is:
y = 1/2x - 2