Answer:
y - 4 = -4(x+2)
Explanations:
The equation of a line in point-slope form is given as shown below;
[tex]y-y_1=m(x-x_1)[/tex]
where;
m is the slope
(x1, y1) is any point on the line
Given the following parameters
(x1, y1) = (-2, 4)
Determine the slope of the line using the coordinates (0, -4) and (-2, 4)
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{4-(-4)}{-2-0} \\ m=\frac{4+4}{-2} \\ m=-\frac{8}{2} \\ m=-4 \end{gathered}[/tex]
Substitute the slope and the point into the formula above to have:
[tex]\begin{gathered} y-4=-4(x-(-2)) \\ y-4=-4(x+2) \end{gathered}[/tex]
This gives the required equation in point-slope form
