slope that runs through points (2,9) (6,-4)

Question

what is the slope that runs through the points (2,9) & (6,-4) I can't understand it please help

Answer 1

Slope is often described as   being rise/run  as we go from point 1 to point 2.

     The rise is the change in the y coordinate, the run is the change in the x coordinate.

           { "change in"   means take the difference  }

     The rise can actually be negative in some cases (including this one)

     The run can also be negative   (but not in this case)

 

If we think of the point  (2,9)  as point 1 and (6, -4) as point 2 ,

 

then in going from point 1 to point 2 , the change in y = -4 - 9  =  -13  { the rise, which is negative}

and the  change in x = 6 - 2  =  4      {the run}  .

 

Thus the slope is  -13/4  .      

This a negative number because the "rise" was negative (i.e. could  be thought of as a decline)