How do you write the point slope form of the equation given (3,-3) and (5,0)?

First, we need to determine the slope of the line represented by the two points in the problem. The slope can be found by using the formula: #m = (color(red)(y_2) - color(blue)(y_1))/(color(red)(x_2) - color(blue)(x_1))#

Where #m# is the slope and (#color(blue)(x_1, y_1)#) and (#color(red)(x_2, y_2)#) are the two points on the line.

Substituting the values from the points in the problem gives:

#m = (color(red)(0) - color(blue)(-3))/(color(red)(5) - color(blue)(3)) = (color(red)(0) + color(blue)(3))/(color(red)(5) - color(blue)(3)) = 3/2#

The point-slope formula states: #(y - color(red)(y_1)) = color(blue)(m)(x - color(red)(x_1))#

Where #color(blue)(m)# is the slope and #(color(red)(x_1, y_1))# is a point the line passes through.

Substituting the slope we calculated and the values from the first point gives:

#(y - color(red)(-3)) = color(blue)(3/2)(x - color(red)(3))#

#(y + color(red)(3)) = color(blue)(3/2)(x - color(red)(3))#

We can also substitute the slope we calculated and the values from the second point giving:

#(y - color(red)(0)) = color(blue)(3/2)(x - color(red)(5))#

Or

#y = color(blue)(3/2)(x - color(red)(5))#