How do to work out the $y$-intercept from a given coordinate and a gradient?

Question

The question gives a gradient, $2$, and a coordinate, $(0,-1)$, which the line slopes through. Essentially I need to put this into an equation: $$y=mx+c.$$

I understand that it would be $y=2x+c$, but what is $c$? Furthermore how do I work it out from just $1$ coordinate given?

Answer 1

Oh, very easy. That the point with coordinates $(0,-1)$ lies on the line, means exactly that substituting $x=0$ and $y=-1$ in the equation of the line will give a true sentence: $$-1=2\cdot 0+c$$