Question

What is the equation of the line, in general form, that passes through (1, 2) and is parallel to the line whose equation is 3x - 4y + 12 = 0?

Answer 1

The answer is: 3 x - 4 y + 5 = 0

y = (3/4) x + 5/4 written in standard form is 3 x - 4 y + 5 = 0.

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Answer 2

Parallel lines have same slope
3x - 4y + 12 = 0
4y = 3x + 12
y = 3/4 x + 3
so the slope is 3/4

general form of the line is y=mx+c
if the line passes through this point (1,2) and has the slope of 3/4
y = mx + c
2 = (3/4)*1 + c
c = 2 - (3/4)
c = 5/4

therefore the general form of the line is
y = (3/4)x + 5/4