Question

8,-4);3x-5y=8 slope parallel ?

Answer 1

Let us first bring the equation given into the slope-intercept form.

$\begin{gathered} 3x-5y=8, \\ 5y=3x-8, \\ \rightarrow\textcolor{#FF7968}{y=\frac{3}{5}x-\frac{8}{5}.} \end{gathered}$

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

$y=\frac{3}{5}x+b$

where b is the y-intercept yet unknown.

Let us plug in (x, y) = (8, -4) in the above equation, this gives

$-4=\frac{3}{5}(8)+b$$-4=\frac{24}{5}+b$$\therefore b=-\frac{44}{5}\text{.}$

Hence, the equation of the line in slope-intercept form is

$\textcolor{#FF7968}{y=\frac{3}{5}x-\frac{44}{5}}\text{\textcolor{#FF7968}{.}}$