What is the point-slope form of the line that passes through (-2,1) and (5,6)?

1 Answer
May 1, 2018

Answer:

The point-slope formula is #y##1# =#m##(x + 2)#, where #m# is #5/7#.

Explanation:

First, start with your point-slope formula:

#y##y_1# =#m##(x−x_1)#

Label your ordered pairs:

#(-2, 1)# = #(X_1, Y_1)#
#(5, 6)# = #(X_2, Y_2)#

#y##1# =#m##(x−-2)#

Two negatives make a positive, so, this is your equation:

#y# - #1# = #m##(x+2)#


Here's how to solve for #m# to plug-it into your point-slope formula:

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

Now, label your ordered pairs as #X_1#, #X_2#, #Y_1#, and #Y_2#:

#(-2, 1)# = #(X_1, Y_1)#
#(5, 6)# = #(X_2, Y_2)#

Now, plug your data into the formula:

#(6 - 1)/(5 - - 2)# = #m#

5 - - 2 becomes 5 + 2 because two negatives create a positive. Now, the equation is:

#(6 - 1)/(5+2)# = #m#

Simplify.

#5/7# = #m#

Therefore, #m# = #5/7#.