The equation of a line in standard form is written as:
[tex]Ax+By=C[/tex]
Now, two lines are parallel if and only if their slopes are equal, that is:
[tex]m_1=m_2[/tex]
The slope of a line is given by:
[tex]m=\frac{y_2-y_1_{}}{x_2-x_1}[/tex]
where (x1,y1) and (x2,y2) are points through the line. From the graph we notice that the line passes through the points (0,3) and (5,-1) then its slope is:
[tex]\begin{gathered} m=\frac{-1-3}{5-0} \\ m=-\frac{4}{5} \end{gathered}[/tex]
This means that the lin in the graph has a slope os -4/5 and hence the paralell line we are looking for has slope -4/5 as well.
Once we know the slope of the line we want we just need a point; the porblem states that the line passes through the origin, then it passes through the point (0,0). The equation of a line with slope m that passes throught the point (x1,y1) is given by:
[tex]y-y_1=m(x-x_1)[/tex]
Plugging the values of the slope and the point we have that:
[tex]\begin{gathered} y-0=-\frac{4}{5}(x-0) \\ y=-\frac{4}{5}x \end{gathered}[/tex]
Finally we just write the equation in standard form, therefore the equation of the line is:
[tex]\frac{4}{5}x+y=0[/tex]
