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

1 Answer
Jul 22, 2015

2y = 3(x - 4) + 10

Explanation:

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