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You have the following equation:

9x - 5y = 6

In order to find the equation of the line, you first calculate the slope of the previous line equation:

9x - 5y = 6 subtract 9x both sides

9x - 9x - 5y = 6 - 9x simplify

-5y = -9x + 6 divide by -5 both sides

-5y/(-5) = -(9/5)x + 6/5 simplify

y = -(9/5)x + 6/5

y = -1.8x + 1.2

Then, the slope of the line is m=-1.8

Now, to find the equation of the line with the point (6,-2) you use the following formula for the slope of a line:

m=(y-yo)/(x-xo)

due to the required line is parallel to the line with slope -1.8, the slope of the required line is the same, m = -1.8. xo and yo are the given coordiantes of the given point (6,-2), that is, xo = 6 and y = -2. You replace these values into the formula for the slope and solve for y:

m = (y - (-2))/(x - 6) = (y + 2)/(x - 6) multiply both sides by (x-6)

(x-6) m= y + 2

y = mx - 6m - 2 = (-1.8)x - 6(-1.2) - 2

y = -1.8x - 5.2

This last equation is the required equation

User Heinrisch
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