Answer: [tex]y+4=-3(x-3)[/tex]
Step-by-step explanation:
The point-slope equation of a straight line is:
[tex]y-y_{1}=m(x-x_{1} )[/tex]
where m is the slope and [tex](x_{1}, y_{1} )[/tex] are the coordinates of a point in the line.
So, to find the equation, the firs step is to find the slope. We can see in the graphic that the line intercepts the y axis at the point (0, 5), so we're going to use that and the other given point to find the slope:
[tex]m=\frac{y_{2}-y_{1} }{x_{2}-x_{1}} =\frac{-4-5}{3-0} =\frac{-9}{3}=-3[/tex]
Then, you simply substitute the slope and the coordinates of the point and you get the point-slope equation:
[tex]y-(-4)=-3(x-3)\\y+4=-3(x-3)[/tex]
