The general line equation in slope-intercept form is given by
[tex]y=mx+b[/tex]where b is the y-intercept and m is the slope. In our case, we have the points
[tex]\begin{gathered} (x_1,y_1)=(0,0) \\ (x_2,y_2)=(3,4) \end{gathered}[/tex]and the slope m is given by
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]by substituting our point into this formula,we get
[tex]\begin{gathered} m=\frac{4-0}{3-0} \\ m=\frac{4}{3} \end{gathered}[/tex]then, our line equation has the form
[tex]y=\frac{4}{3}x+b[/tex]We can find b by substituting point (0,0) in this last equation. It yields,
[tex]\begin{gathered} 0=\frac{4}{3}(0)+b \\ b=0 \end{gathered}[/tex]Then, the line equation is
[tex]y=\frac{4}{3}x[/tex]which corresponds to option A.