Write an equation in slope-intercept form for a line that passes through (5,-8) and is parallel to $5x+6y=21$ .

A) $y=\frac{6}{5}x-\frac{23}{6}$
B) $y=-\frac{5}{6}x-\frac{23}{6}$
C) $y=\frac{5}{6}x+\frac{23}{6}$
D) $y=-\frac{5}{6}x-\frac{43}{6}$
E) $y=-\frac{6}{5}x-\frac{23}{6}$

First, convert the given equation $5x+6y=21$ to slope-intercept form to find the slope of the parallel line. The slope-intercept form is $y=mx+b$ , where $m$ is the slope. The given equation becomes $6y=-5x+21$ , so $y=-\frac{5}{6}x+\frac{21}{6}$ . Parallel lines have the same slope, so the slope of the line we're looking for is $-\frac{5}{6}$ . To find the y-intercept ( $b$ ), use the point (5, -8) and the slope $-\frac{5}{6}$ in the equation $y=mx+b$ , which gives $-8=-\frac{5}{6}(5)+b$ . Solving for $b$ gives $b=-\frac{23}{6}$ . Therefore, the equation of the line is $y=-\frac{5}{6}x-\frac{23}{6}$ .