Answer:
5x + 3y = 12
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