# How to find b in linear equation form y=mx+b if the 2 coordinates are (5,6) and (1,0)?

Apr 14, 2018

color(blue)(y = (3/2)x - (3/2)

color(purple)( " is the slope-intercept form of equation with slope = 3/2, y-intercept = -3/2"

#### Explanation:

$\left({x}_{1} , {y}_{1}\right) = \left(5 , 6\right) , \left({x}_{2} , {y}_{2}\right) = \left(1 , 0\right)$

Equation of line is $\frac{y - {y}_{1}}{{y}_{2} - {y}_{1}} = \frac{x - {x}_{1}}{{x}_{2} - {x}_{1}}$

$\frac{y - 6}{0 - 6} = \frac{x - 5}{1 - 5}$

$\frac{y - 6}{\cancel{- 6}} ^ \textcolor{red}{3} = \frac{x - 5}{\cancel{- 4}} ^ \textcolor{red}{2}$

$2 y - 12 = 3 x - 15 , \text{ cross multiplying}$

$2 y = 3 x - 15 + 12$

Standard form of slope-intercept equation is color(indigo)(y = mx + c
color(blue)(y = (3/2)x - (3/2)

color(purple)( " is the slope-intercept form of equation with slope = 3/2, y-intercept = -3/2"