For this case we have that the equation of a line of the point-slope form is given by:
[tex](y-y_ {0}) = m (x-x_ {0})[/tex]
To find the slope we look for two points through which the line passes:
We have to:
[tex](x1, y1) :( 0,2)\\(x2, y2) :( 4, -2)[/tex]
Thus, the slope is:
[tex]m = \frac {y2-y1} {x2-x1} = \frac {-2-2} {4-0} = \frac {-4} {4} = - 1[/tex]
Substituting a point in the equation we have:
[tex](y - (- 2)) = - 1 (x-4)\\y + 2 = - (x-4)[/tex]
Answer:
Option A
