Answer
$y=-5x-6$
Work Step by Step
Let $(-2,4)=(x_{1}, y_{1})$ and $(0,-6)=(x_{2}, y_{2})$
The gradient of a line is given by the equation:
gradient$=\frac{ y_{2}- y_{1}}{x_{2}-x_{1}}$
By substituting in the given points, the gradient, $m$, of the line is:
$\frac{(-6)-(4)}{0)-(-2)}$
$=\frac{-10}{2}=-5$
The equation for a line is given by:
$y-y_{1}=m\times(x-x_{1})$
Substituting $m=-5$ and $(x_{1}, y_{1})=(0,-6)$
$y-(-6)=-5(x-0)$
The expression can then be simplified to $y+6=-5x$
Subtracting $6$ from both sides, the solution $y=-5x-6$ is obtained.
