Find the equation of the line.

Question

Find the equation of the line passing through the point $(5,7)$ and parallel to the line $5x+4=0$

If I say $m=5$, how should I find $c$? There is no $y$ in the equation!

Answer 1

Your slope of $5$ is wrong. $5x+4=0\implies x=-\frac{4}{5}$. Constant $x$ means that the line is perpendicular to the $x$-axis. Any line parallel to this, will also be perpendicular to the $x$-axis, implying that it will have constant $x$.

Finally we already know the value of that $x$, since a point lying on the line, $(5,7)$ is known. Thus the required equation of line is $x=5$