# Line AB passes through points A (6,6) and B(12, 3). If the equation of the line is written in slope-intercept form, y=mx+b, what is m and b?

Dec 1, 2016

$m = - 2 , \text{ } b = 18$

#### Explanation:

eqn. of a straight line with known co-ordinates

$\left({x}_{1} , {y}_{1}\right) , \text{ } \left({x}_{2} , {y}_{2}\right)$

is given by the formula

$\frac{y - {y}_{1}}{x - {x}_{1}} = \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}$

for $A \left(6 , 6\right) , \text{ } B \left(12 , 3\right)$

$\frac{y - 6}{x - 6} = \frac{12 - 6}{3 - 6}$

$\frac{y - 6}{x - 6} = \frac{6}{-} 3 = - 2$

$y - 6 = - 2 \left(x - 6\right)$

$y = 6 + \left(- 2 x\right) + 12$

$y = - 2 x + 18$

$m = - 2 , \text{ } b = 18$