The goal of this question is to find the slope from two ordered pairs (two points on the graph). To do this, use this equation:

#(Y_2 - Y_1)/(X_2 - X_1)# =#m#, the slope

Next, let's label our ordered pairs, or points, as #X_1#, #Y_1#, #X_2#, and #Y_2#. List your ordered pairs. Recall that an ordered pair is in the form #(x, y)#.

#(5, -3)# #(X_1, Y_1)#

#(2, 5)# #(X_2, Y_2)#

Now, plug this information into your equation:

#(Y_2 - Y_1)/(X_2 - X_1)# =#m#

#(5 - -3)/(2 - 5)# = #m#

Two negatives make a positive, so:

#(5 + 3)/(2 - 5)# = #m#

Simplify.

#(8)/(-3)# = #m#

The slope, #m#, is #(8, -3)#. If you want to continue to find the whole line in the form of #y = mx + b#, use the point-slope formula as shown below. Recall that #m# is the slope and the ordered pair you'll be using is the one you labeled as #(X_1, Y_1)#.

#(y - y_1) = m(x - x_1)#

Plug in your information:

#(y - -3) = (8/-3)(x - 5)#

Distribute:

#(y + 3) = (8/-3x) + (-40/3)#

Subtract 3 from both sides to isolate for y:

#y = (8/-3x) + (49/-3)#

Remove parentheses:

#y = 8/-3x + 49/-3#