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

Question

Isaiah Anthony · Accepted Answer

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#.

Eva Abramson · Answer

undefined The point-slope form of the line passing through (-2,1) and (5,6) is y - y₁ = m(x - x₁), where m is the slope and (x₁, y₁) is a point on the line. To find the slope, you use the formula m = (y₂ - y₁) / (x₂ - x₁), where (x₁, y₁) = (-2,1) and (x₂, y₂) = (5,6). So, m = (6 - 1) / (5 - (-2)) = 5 / 7. Now, using one of the points and the slope, you can substitute into the point-slope form: y - 1 = (5/7)(x - (-2)). Simplifying, you get y - 1 = (5/7)(x + 2).