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write the equation of the line containing the points (3, 5) and (–3, 0) in slope-intercept form. show all work

The equation of a line containing the point (x1,y1) and haveing a slope of m is
y-y1=m(x-x1)

to convert to slope-intercept (y=mx+b), just solve for y

so

slope between 2 points (x1,y1) and (x2,y2) is (y2-y1)/(x2-x1)

given
(3,5) and (-3,0)
slope=(0-5)/(-3-3)=-5/-6=5/6
m=5/6

use any point
let's use (-3,0)
(x1,y1)
y-y1=m(x-x1)
y-0=5/6(x-(-3))
y=5/6(x+3)
y=5/6x+15/6
y=5/6x+5/2