How do you write an equation in standard form with integer coefficients for the line with slope 17/12 going through the point (-5,-3)?

May 3, 2018

$17 x - 12 y = - 49$

Explanation:

The equation is like that:
$y = m x + b$
$m$ is the slope which equals to $\frac{17}{12}$
$x = - 5$
$y = - 3$
$b$ is the intercept.

So
$- 3 = \frac{17}{12} \cdot \left(- 5\right) + b$
$- 3 = - \frac{85}{12} + b$
$- 3 + \frac{85}{12} = b$
$- \frac{36}{12} + \frac{85}{12} = b$
$\frac{49}{12} = b$

An equation in standard form:
$y = \frac{17}{12} x + \frac{49}{12}$
$y \cdot 12 = \frac{17}{12} \cdot 12 + \frac{49}{12} \cdot 12$
$12 y = 17 x + 49$
$17 x - 12 y = - 49$