How do you write an equation in point-slope form for the given (4, 5), (2, 2)?

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Answer 1 · 2015-07-22T18:44:51

#2y = 3(x - 4) + 10#

You want the line AB, given A and B, don't you?

#A = (x_a, y_a)#

#B = (x_b, y_b)#

#(\Delta y) / (\Delta x) = (y_b - y_a) / (x_b - x_a) = m#

#AB: y = mx + k#

#A \in AB \Rightarrow y_a = mx_a + k#

#k = y_a - mx_a#

Therefore #AB: y = mx - mx_a + y_a#

#y = m(x - x_a) + y_a#

With your numbers,

#m = (2 -5)/(2 - 4) = 3/2, y = 3/2 (x - 4) + 5#