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

Jul 22, 2015

$2 y = 3 \left(x - 4\right) + 10$

#### Explanation:

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

$A = \left({x}_{a} , {y}_{a}\right)$

$B = \left({x}_{b} , {y}_{b}\right)$

$\frac{\setminus \Delta y}{\setminus \Delta x} = \frac{{y}_{b} - {y}_{a}}{{x}_{b} - {x}_{a}} = m$

$A B : y = m x + k$

$A \setminus \in A B \setminus R i g h t a r r o w {y}_{a} = m {x}_{a} + k$

$k = {y}_{a} - m {x}_{a}$

Therefore $A B : y = m x - m {x}_{a} + {y}_{a}$

$y = m \left(x - {x}_{a}\right) + {y}_{a}$

$m = \frac{2 - 5}{2 - 4} = \frac{3}{2} , y = \frac{3}{2} \left(x - 4\right) + 5$