Answer:
y = -5x/6 - 33/6
Explanation:
The standard form of equation of a line in point slope form is y - y0 = m(x - x0)
m is the slope
(x0, y0) is the point on the line
First we need the slope of the given equation 5x+6y=11.
Rewrite in standard form;
5x+6y=11
6y = -5x + 11
y = -5/6 x + 11/6
Hence the slope is -5/6
Since the unknown line is parallel to this line, they will have the same slope, hence the slope of the required line is -5/6
Substitute m = -5/6 and the point (-5,-3) into the point-slope expression;
y - y0 = m(x - x0)
y - (-3) = -5/6 (x - (-5))
y + 3 = -5/6(x+3)
6(y+3) = -5(x+3)
6y+18 = -5x - 15
6y+5x =-15 -18
6y+5x =-33
Express in slope intercept form
6y = -5x - 33
y = -5x/6 - 33/6