Question

Write the equation of the line that passes through (0, 3) and is parallel to the line 3x + 5y = 6.

Answer 1

There's more ways than one to solve this, just as there's more ways than one to skin a cat.

Two paralle lines have the same slope, so the desired new line looks exactly like the given line 3x + 5y = 6, except that the constant, 6, is replaced by another value.

Write out 3x + 5y = c
Replace x with 0 and y with 3.  Then 3(0) + 5(3) = c, and c = 15.

Thus, the equation of the new, parallel, line is 3x + 5y = 15.