First, we need to find the line equation of the given graph. In our to do it, we can choose 2 points along the line, for instance,
[tex]\begin{gathered} (x_1,y_1)=(-1,-2) \\ (x_2,y_2)=(0,2) \end{gathered}[/tex]
Then, the slope is given by
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{2-(-2)}{0-(-1)}=\frac{4}{1}=4 \end{gathered}[/tex]
And we can note that the y-intercept is y=2. Thefore, the line equation is
[tex]y=4x+2[/tex]
By comparing thsi result with the given options, the equations with larger y-intercept and smaller rate are:
[tex]\begin{gathered} y=\frac{1}{5}x+3 \\ \\ y=2x+5 \end{gathered}[/tex]
