a line with slope -2 that passes through the point (3,-3)

A very useful equation to know is the point-slope form for a straight line:

     y - y1  =  m(x - x1)

where  m  is the slope and  (x1, y1) are the coordinates of the point.

For this problem,  m = -2,  x1 = 3,  and  y1 = -3.

Putting these values into the formula:  y - -3  =  -2(x - 3)

Simplifying:  y + 3  =  -2x + 6     --->     y  =  -2x + 3