Question

which of the following is the equation of a line with a slope of -5/9 and passing through the point (9,6)

Answer 1

Given the slope and a point on the line, use the point-slope formula for the equation of a straight line.

y-6 = (-5/9)(x-9)

This can be put into other forms.  For example, 

             Multiplying all terms by 9 results in   9y - 54 = -5(x-9) = -5x + 45

             Solving for y:  9y - 54 = -5x + 45
                                          +54 =        +54
                                      ---------------------------
                                         9y = -5x + 99

Then y = (-5/9)x + 11.