First off, remember that parallel lines always have the same slope. If they have the same slope, then let's find the slope of the line we have so we can use it.
[tex]6x-9y=-7\\-9y=-6x-7\\y=\frac{-6}{-9}x+\frac{-7}{-9}\\y=\frac{2}{3}x+\frac{7}{9}[/tex]
The equation for a line in slope-intercept form is y = mx + b, where m is the slope of the line and b is the y-intercept.
If [tex] y=\frac{2}{3}x+\frac{7}{9} and [tex]y=mx + b[/tex], then m = slope = 2\3.
Thus, the slope of the line is 2/3.
So now we know that m = 2/3, but we don't know what b equals...
Oh wait, we have an equation that contains m, x, y, and b, and using the point (8, 2) we now have (x, y) and can plug those into the equation [tex]y = mx +b [/tex]
[tex] y=mx+b\\(2)=(\frac{2}{3})(8)+b\\2=\frac{16}{3}+b\\b=2-\frac{16}{3}=\frac{6}{3}-\frac{16}{3}=\frac{-10}{3}\\\\b=\frac{-10}{3}[/tex]
So now we know both m and b, so plug them into the equation of a line in slope-intercept form:
[tex] y= mx+b\\y=(\frac{2}{3})x+(\frac{-10}{3})\\\\y=\frac{2}{3}x-\frac{10}{3}[/tex]
