Presumably we're after the line with that slope through that point. In general the line through [tex](a,b)[/tex] with slope [tex]m[/tex] is
[tex]y-b = m(x-a)[/tex]
Here we have [tex]a=-3, b=1, m=\frac 2 5[/tex]
[tex]y - 1 = \frac 2 5 (x--3)[/tex]
[tex]y = \frac 2 5 x + \frac 6 5 + 1[/tex]
[tex]y = \frac 2 5 x + \frac{11}{5}[/tex]
Check: The slope is clearly [tex]\frac 2 5[/tex]
so we check
[tex]y = \frac 2 5 (-3) +\frac{11}{5} = \frac 5 5 = 1 \quad\checkmark[/tex]
