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

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Answer 1 · 2018-05-01T18:51:09

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

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#.