We are asked to determine the equation of a line that passes through the point (-3, -1) and has a slope 2/5. To do that we will use the point-slope form of a line equation:
[tex]y-y_0=m(x-x_0)[/tex]Where:
[tex]\begin{gathered} (x_0,y_0)=\text{ point on the line} \\ m=\text{ slope} \end{gathered}[/tex]Now, we plug in the values:
[tex]y-(-1)=\frac{2}{5}(x-(-3))[/tex]Simplifying we get:
[tex]y+1=\frac{2}{5}(x+3)[/tex]Now, we apply the distributive law:
[tex]y+1=\frac{2}{5}x+\frac{6}{5}[/tex]Now, we subtract 1 from both sides:
[tex]\begin{gathered} y=\frac{2}{5}x+\frac{6}{5}-1 \\ \\ y=\frac{2}{5}x+\frac{1}{5} \end{gathered}[/tex]and thus we get the equation of the line.
