General form of a line : [tex]Ax + By + C = 0[/tex]
The slope-intercept form: [tex]y=mx+b[/tex]
m - slope
b - y-intercept
We have
a slope [tex]\to m=-\dfrac{1}{3}[/tex] and y-intercept[tex]\to b=\dfrac{10}{3}[/tex].
Substitute:
[tex]y=-\dfrac{1}{3}x+\dfrac{10}{3}[/tex] multiply both sides by 3
[tex]3y=-x+10[/tex] subtract 3y from both sides
[tex]0=-x-3y+10[/tex] change the signs
[tex]\boxed{x+3y-10=0}[/tex]
