What is the equation of the line with slope  m= 17/3  that passes through  (7/9,8/3) ?

Nov 28, 2015

In slope point form: $\left(y - \frac{8}{3}\right) = \left(\frac{17}{3}\right) \left(x - \frac{7}{9}\right)$

In standard form: $153 x - 27 y = 47$

Explanation:

The general slope-point form for a line with slope $m$ through a point $\left(\hat{x} , \hat{y}\right)$ is
$\textcolor{w h i t e}{\text{XXX}} \left(y - \hat{y}\right) = m \left(x - \hat{x}\right)$

For the given values this becomes:
$\textcolor{w h i t e}{\text{XXX}} \left(y - \frac{8}{3}\right) = \left(\frac{17}{3}\right) \left(x - \frac{7}{9}\right)$

To convert this to standard form we will need to do some simplification.

Begin clearing the denominators by multiplying both sides by $3$
$\textcolor{w h i t e}{\text{XXX}} 3 y - 8 = 17 \left(x - \frac{7}{9}\right)$
Continue clearing the denominators by multiplying both sides by $9$
$\textcolor{w h i t e}{\text{XXX}} 27 y - 72 = 17 \left(9 x - 7\right) = 153 x - 119$

Subtract $\left(153 x\right)$ from both sides
$\textcolor{w h i t e}{\text{XXX}} - 153 x + 27 y - 72 = - 119$

Add $72$ to both sides
$\textcolor{w h i t e}{\text{XXX}} - 153 x + 27 y = - 47$

Multiply both sides by $\left(- 1\right)$
$\textcolor{w h i t e}{\text{XXX}} 153 x - 27 y = 47$