# What is the equation of the line with slope  m= -17/25  that passes through  (47/5 32/10) ?

Jul 5, 2018

$y = - \frac{17}{25} \cdot x + \frac{1199}{125}$

#### Explanation:

Such an equation has the form

$y = m x + n$ where $m$ is the slope and $n$ the y intercept.

So we get
$y = - \frac{17}{25} \cdot x + n$
plugging $x = \frac{47}{5}$ and $y = \frac{32}{10}$ in the equation above we can calculate $n$:

$\frac{32}{10} = - \frac{17}{25} \cdot \left(\frac{47}{5}\right) + n$

doing this we get

$n = \frac{1199}{125}$

Jul 5, 2018

color(indigo)(85x + 125y + 424 = 0

#### Explanation:

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

$\text{Given : " (x_1, y_1) = (47/5, 32/10), " Slope } = m = - \frac{17}{25}$

color(crimson)((y - 32/10) = (-17/25) * (x - 47/5)

$\left(10 y - 32\right) \cdot 125 = - 17 \cdot 10 \cdot \left(5 x - 47\right)$

$1250 y - 3750 = - 850 x - 7990$

$850 x + 1250 y = - 7990 + 3750 = - 4240$

color(indigo)(85x + 125y + 424 = 0