Find the equation of the line which passes through the point (6, -4) and is parallel to to the line 2x-3y+3=0.

Question

Please show working out as well, thanks.

Answer 1

3y = 2 x + 3
is
y = (2/3)x + 1
slope = 2/3
so
y = (2/3)x + b if parallel

-4 = (2/3)6 + b
b = -8
so
y = (2/3)x-8
3 y = 2 x - 24

Answer 2

The slope of 2x-3y+3=0 is 2/3.
The parallel line you want has a slope of 2/3 and passes through (6,-4)

So, using the point-slope form of the line,

y+4 = 2/3 (x-6)