Answer:
[tex]y+2 = x+2[/tex]
Step-by-step explanation:
A line is written in the point-slope form if its equation is in the form
[tex]y-y_1 = m(x-x_1)[/tex]
where
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex] is the slope of the line, calculated using the two points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]
In this problem, we have the following two points:
[tex](x_1,y_1) = (-2,-2)\\(x_2,y_2)=(2,2)[/tex]
Therefore we can calculate the slope of the line:
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{2-(-2)}{2-(-2)}=\frac{4}{4}=1[/tex]
And so, the equation of the line in point-slope form is
[tex]y-(-2) = 1(x-(-2))\\\rightarrow y+2 = x+2[/tex]
