Question

What is the equation of the line that passes through (–2, 3) and is parallel to 2x + 3y = 6?

Answer 1

If you know that the equation is parallel to 2x+3y=6, it must have the same slope (so that it'll never touch, right?).
To find the slope of the given line, put it into slope-intercept form, so you get
3y=-2x+6
y=-2/3x+2
slope= -2/3

substitute that into y=mx+b, as the b-value.
y=-2/3x+b

now to solve for the equation that runs through the point (-2, 3), you need to substitute that as the x- and y-values and solve for b

3=(-2/3)(-2)+b
3=4/3+b
5/3=b

substitute the b-value into the equation where it is just y=-2/3x+b to get your final function

y=-2/3x+5/3

and if you need to put this in standard form, it becomes
y+2/3x=5/3
3y+2x=5

Answer 2

but these are the answers

Answer 3

A.y=-3/2x -6
B.y=-2/3x + 6
C.y=2x + 3
D.y=3/2x