Question

Write an equation of the line that is parallel to 3x + 9y = 7 and passes through the point (6, 4).

Answer 1

First, rearrange the equation to standard line format
3x + 9y = 7
9y = -3x + 7
y = -3/9x + 7/9
y = -1/3x + 7/9

now we know the slope of the line (both the existing and the new parallel one, since they both have the same slope)

y = -1/3x + b

plug in the new point in and solve for b

4 = -1/3(6) + b
4 = -2 + b
b = 6

y = -1/3x + 6 is the equation for the parallel line