# What is the equation of the line with slope  m= 6/25  that passes through  (-1/5 -32/10) ?

May 20, 2016

$y = \frac{6}{25} x + \frac{394}{125}$

#### Explanation:

Straight line equation standard form $y = m x + c$

Given that:
$m = \frac{6}{25}$

point ${P}_{1} \to \left(x , y\right) \to \left(- \frac{1}{5} , - \frac{32}{10}\right)$

Substituting known values

color(brown)(y=mx+c)color(blue)(" "-> " "-32/10=6/25(-1/5)+c

$\implies - \frac{32}{10} = - \frac{6}{125} + c$

Add $\frac{6}{125}$ to both sides

$- \frac{32}{10} + \frac{6}{125} = c$

$c = - 3 \frac{19}{125} \to \frac{394}{125}$
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So the equation becomes

$y = \frac{6}{25} x + \frac{394}{125}$