Respuesta :
Let us first bring the equation given into the slope-intercept form.
[tex]\begin{gathered} 3x-5y=8, \\ 5y=3x-8, \\ \rightarrow\textcolor{#FF7968}{y=\frac{3}{5}x-\frac{8}{5}.} \end{gathered}[/tex]We see that the above equation has slope 3/ 5, and therefore, the equation that we want to construct must also have this slope. Hence, we already know that the equation we are seeking must take the form
[tex]y=\frac{3}{5}x+b[/tex]where b is the y-intercept yet unknown.
Let us plug in (x, y) = (8, -4) in the above equation, this gives
[tex]-4=\frac{3}{5}(8)+b[/tex][tex]-4=\frac{24}{5}+b[/tex][tex]\therefore b=-\frac{44}{5}\text{.}[/tex]Hence, the equation of the line in slope-intercept form is
[tex]\textcolor{#FF7968}{y=\frac{3}{5}x-\frac{44}{5}}\text{\textcolor{#FF7968}{.}}[/tex]