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Answer:

5x + 3y = 12

Step-by-step explanation:

We are given the line 5x + 3y = 6 and are to find the equation of a new line that is parallel to this one and goes through (3, -1).

Parallel lines have the same slope.  The slope of the given line is determined by the coefficients 5 and 3 visible above.  Therefore, the form of the equation of the new line is 5x + 3y = C, where we must determine the value of C.

Substitute 3 for x and -1 for y in 5x + 3y = C, obtaining:  5(3) + 3(-1) = C.  Then 15 - 3 = 12 is the constant value, and the equation of the 'new line' is

5x + 3y = 12

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