What is the equation of the line that passes through (4, 2) and is parallel to 3x - 2y = -6?
-x+
-x
x-4

The Answer is: The point slope form of the equation that is parallel to the given equation and passes through the point (4, 2) is: y = 3/2x - 4

Step-by-step explanation:

Given point: (4, 2)

Given equation:

3x - 2y = -6

Solve for y, to obtain slope m:

-2y = -6 - 3x

y = 3/2x + 3, so the slope m = 3/2. A parallel line has the same slope.

Use the point slope form and substitute the point (4, 2):

y - y1 = m(x - x1)

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

y - 2 = 3/2x - 6

y = 3/2x - 6 + 2

y = 3/2x - 4

Proof:

Find f(x) for x = 4

f(x) = 3/2(4) - 4

f(x) = 6 - 4 = 2, giving the point (4, 2)

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