Answer
(a) $y=-\frac{6}{5}x+6$
(b) $slope=m=-\frac{6}{5}$
(c) $y-intercept=b=6$; point $(0,6)$
(d) See graph.
Work Step by Step
(a)
A line in slope-intercept form has the equation:
$y=mx+b$ ($m=slope$, $b=y-intercept$)
We put the equation into slope-intercept form:
$6x+5y=30$
$5y=30-6x$
$y=6-6/5x$
$y=-\frac{6}{5}x+6$
(b) We see that $slope=m=-\frac{6}{5}$
(c) We see that $y-intercept=b=6$; point $(0,6)$
(d) See graph.