Verified answer

3x + 2y = 4

2y = 4 - 3x

y = 2 - 3/2 x

Slope = -3/2

y = mx + b

y = -3/2 x + b

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

b = -1

Answer...y = -3/2 x - 1

Parallel lines have equal slope, so 1st find the slope of the given line:

3x+2y=4

2y=4-3x

y=-3x/2+2

Slope = -3/2

Use that and the point to find b for the new equation:

y=mx+b

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

-4 = -3+b

-1 = b

y = (-3/2)x-1

For the same slope, we keep the same coefficients on x and y.

So we have:

3x + 2y = c

To find c, we plug in the values we have for x and y:

3(2) + 2(-4) = c

6 - 8 = c

-2 = c

So our final equation (in the same form as the original equation) is:

3x + 2y = -2

If you want that in slope-intercept form, solve for y:

3x + 2y = -2

2y = -3x - 2

y = (-3/2) x - 1