For this case we have that by definition, the equation of a line of the slope-intersection form is given by:
[tex]y-y_{0}=m(x-x_{0})[/tex]
Where:
m: It is the slope of the line
[tex](x_ {0}, y_ {0})[/tex]: It is a point through which the line passes.
We have to:
[tex]m = -2[/tex]
Thus, the equation is of the form:
[tex]y-y_{0}=-2(x-x_{0})[/tex]
We substitute the point [tex](x_{0}, y_{0}) :( 4, -6)[/tex]
[tex]y-(-6)=-2(x-4)\\y+6=-2(x-4)[/tex]
Finally, the equation is:
[tex]y+6=-2(x-4)[/tex]
Answer:
[tex]y = -2x + 2[/tex]
[tex]y+6=-2(x-4)[/tex]
