Question #cf170

To solve this, you can use the point-slope form, which is

#((y_2-y_1)/(x_2-x_1))=m#

when m is equal to slope, and shared subscript denotes the x and y values are from a shared point.

To actually use this formula, you have to assign first and second points. If using the question's points in chronological order, then

#(-14,13)# is the first point, and #(7,0)# is the second, shown as
#(-14,13)_1# and #(7,0)_2#

Now you can replace each variable with its corresponding value
#((y_2-y_1)/(x_2-x_1))=m#
#(((0)-(13))/((7)-(-14)))=m#

Simplify
#(0-13)/(7+14)=m#

Solve
#-13/21=m#

Therefore, the slope is #-13/21#

Slope is equal to #(Deltay)/(Deltax)#, or in other words, change in #y# over change in #x# (The triangle is the Greek letter Delta, which means "change in").

Let's figure out how much did our #x#-value change by:
To get from -14 to 7, we have to add 21, thus #Deltax=21#. This will be our denominator.

#y# went from 13 to 0, so our change in #y#, or #Deltay#, is #-13#. This will be our numerator.

Now we have our slope:

#(Deltay)/(Deltax)=-13/21#