In the future, Ashton, please post only ONE problem at a time. I'm not even sure you want me to start with problem #2, but will address it anyway:
What is the equation of a line that passes through the point (8, −2) and is parallel to the line whose equation is 3x + 4y = 15?
My approach is not the most common one, but in this case it saves time.
If two lines are parallel, their slopes are equal.
The given line is 3x + 4y = 15, and so the equation of a line parallel to this one but passing through the point (8, -2) is the same, EXCEPT that the constant is different (not 15).
Write out 3x + 4y = C and substitute the coordinates of point (8,-2):
3(8) + 4(-2) = C. Then C = 24 - 8, or C=16.
The equation of a line that passes through the point (8, −2) and is parallel to the line whose equation is 3x + 4y = 15 is 3x + 4y = 16.
