Find the equation of the line through the point (1, 16) that is parallel to the given line. Write your final answer in slope-intercept form.
2y – 14x = 12

I think slope intercept form is y = mx + b. So first write the original line like this:

2y = 14x + 12 (add 14x to both sides)
y = 7x + 6 (divide all by 2 so we just have y and not 2y)

Parallel means it has the same slope but different intercept. So we need to know which intercept allows us to have a slope of 7 but go through the point (1, 16).

y = 7x + b
16 = 7(1) + b (substitute x & y)
16 = 7 + b (simplify)
9 = b (subtract 7 on both sides)

So the intercept is 9. So the equation of the parallel line would be y = 7x + 9.

And that answer is parallel to the original line y = 7x + 6; the whole line is shifted upwards by 3 units.