Question

Write a linear equation that is parallel to 12x+3y=24 and passes through the point (-2,7)

Answer 1

In order to write the formula for another line which is parallel, we need the slope (m). Parallel lines never in fact touch or intersect at any one point. They are either the same lines, occupying the same points, or different parallel lines, never occupying the same points, but sharing the same slope (m).
If we put out equation in slope-intercept format: y = mx+b, we can obtain our needed m.
12x+3y=24 ->> 3y = -12x+24
3y/3 = (-12x+24)/3 ->> y = -4x+8, therefore our m = -4
Now we can use our info to make the line in point-slope format: y-y1 = m (x-x1)
So, y-7 = -4 (x--2) or y-7 = -4 (x+2)
You can leave it like that or convert it:
y-7 = -4x -8 ->> y = -4x -8+7 ->> y = -4x-1
or even in this format: 4x+y=-1