Line m goes through a point D(2, -4). Line m is parallel to line l: $5x+3y=-17$. Describe line m with an equation of type $ax+by=c$.
The solution should be $c=5*2+3*-4=-2$ so $\text{m: }5x+3y=-2$
The lines are parallel so $a=5$, $x$ and $y$ are known so: $5*2+b(-4)=c$. At this point I lack some information I should know to push that equation further. I suppose I should be able to fill either $b$ or $c$, but which one and why?
Knowing that they're parallel tells you that they share the same gradient. Try solving it like this and see if you can follow the method;
Rearranging line l into the standard form y = mx + c should show you that the gradient (m) of both lines (since they're parallel) is -(5/3)
Then you have that the equation of line m is;
y = -(5/3)x + c
Substitute in point D(2 , -4) to get c;
-4 = -(5/3)*2 + c
c = -4 + 10/3
c = -2/3
So putting everything into an equation for m, we have;
y = -(5/3)x -2/3
Just rearrange for the form asked for in the question;
(5/3)x + y = -2/3
Or in a little bit nicer form;
5x + 3y = -2