Answer:
Step-by-step explanation:
If we are looking for a line parallel to the given line, we need to find the slope of the given line, since parallel lines have the exact same slope. That means that we need to solve this equation for y, which naturally puts the line into slope-intercept form. Solving for y:
-2y = -4x - 8 and
2y = 4x + 8 so
y = 2x + 4 and the slope, we see here, is 2. Use that slope and the given point of (-1, 4) to write the new equation we need.
In point-slope form, the line will be
y - 4 = 2(x - (-1)) which simplifies a bit to
y - 4 = 2(x + 1). That's point-slope form. Putting it into slope-intercept just requires that we solve this equation for y:
y - 4 = 2x + 2 and
y = 2x + 6. That's slope-intercept form of the same line. The last form is standard, which looks like this:
-2x + y = 6 or, if you don't like to lead with a negative,
2x - y = -6
