#### Answer

(a) $y=-\dfrac{5}{3}x+5$
(b) slope = $-\dfrac{5}{3}$, y-intercept = $5$
(c) Refer to the image below for the graph.

#### Work Step by Step

(a)
The slope-intercept form is $y=mx+b$ where m = slope and b = y-intercept.
Subtract $5x$ on both sides to obtain:
$3y=15-5x
\\3y=-5x+15$
Divide both sides by $3$ to obtain:
$y=\dfrac{-5x+15}{3}
\\y = -\dfrac{5}{3}x + 5$
(b)
The equation has $m=-\dfrac{5}{3}$ and $b=5$.
Thus,
slope = $-\dfrac{5}{3}$
y-intercept = $5$
(c)
Plot the y-intercept point $(0, 5)$.
From $(0, 5)$, move 5 units down (the rise) and 3 units to the right (the run). These steps lead to the point $(3, 0)$.
Connect the two points using a line to complete the graph.