# What is the equation of the line with slope  m= -31/36  that passes through  (-5/6, 13/18) ?

Mar 9, 2018

$216 y + 186 x = 1$

#### Explanation:

Slope of a line $\left(m\right) = \frac{{y}_{1} - {y}_{2}}{{x}_{1} - {x}_{2}}$ ----(1)

Here , $m = - \frac{31}{36}$

${x}_{1} = x$

${x}_{2} = - \frac{5}{6}$

${y}_{1} = y$

${y}_{2} = \frac{13}{18}$

Put these values in equation(1)

$\implies - \frac{31}{36} = \frac{y - \frac{13}{18}}{x - \left(- \frac{5}{6}\right)}$

=> -31/36 = ((18y-13)/cancel18^3)/((6x+5)/cancel6

=> -31/cancel36^12=(18y-13)/(cancel3(6x+5)

Cross-multiply

$\implies - 31 \left(6 x + 5\right) = 12 \left(18 y - 13\right)$

$\implies - 186 x - 155 = 216 y - 156$

$\implies 156 - 155 = 216 y + 186 x$

$\implies 1 = 216 y + 186 x$

Mar 9, 2018

color(orange)(186x + 216y = 1

#### Explanation:

Given slope and a point on the line, we can write the equation using

$\left(y - {y}_{1}\right) = m \left(x - {x}_{1}\right)$

where m is the slope and $\left({x}_{1} , {y}_{1}\right)$ the coordinates of the point.

Hence the equation is

$y - \left(\frac{13}{18}\right) = - \left(\frac{31}{36}\right) \cdot \left(x + \frac{5}{6}\right)$

$y = - \left(\frac{31}{36}\right) x - \left(\frac{31}{36}\right) \cdot \left(\frac{5}{6}\right) + \frac{13}{18}$

$y = \left[\frac{\left(- 31 \cdot 6\right) x - \left(31 \cdot 5\right) + \left(13 \cdot 12\right)}{216}\right]$ L C M 216.

$y = \left[\frac{- 186 x - 155 + 156}{216}\right]$

$y = \frac{- 186 x + 1}{216}$

$216 y = - 186 x + 1$

$186 x + 216 y = 1$