Given the equation;
[tex]\begin{gathered} -\frac{4}{3}x+y=4 \\ -\frac{8}{3}x+2y=-1 \end{gathered}[/tex]
The slope-intercept form is given as;
[tex]y=mx+c[/tex]
Rewriting the equations in slope-intercept form gives;
[tex]\begin{gathered} -\frac{4}{3}x+y=4 \\ y=\frac{4}{3}x+4\ldots.\ldots..\ldots\ldots...\ldots\text{equation 1} \end{gathered}[/tex]
Also;
[tex]\begin{gathered} -\frac{8}{3}x+2y=-1 \\ 2y=\frac{8}{3}x-1 \\ y=\frac{4}{3}x-\frac{1}{2}\ldots\ldots...\ldots\ldots\ldots\text{equation 2} \end{gathered}[/tex]
Equation 1 and equation 2 have an equal solution. Thus, the lines are parallel to each other. In otherwords, the lines cannot intersect.
The graph is;
The equations in slope-interceot form are;
[tex]\begin{gathered} y=\frac{4}{3}x+4 \\ y=\frac{4}{3}x-\frac{1}{2} \end{gathered}[/tex]
