# What is the equation of the line with slope  m= 1/3  that passes through  (-7/15,-5/24) ?

Feb 14, 2016

$y = \frac{x}{3} - \frac{19}{360}$

#### Explanation:

$y = m x + c$

$- \frac{5}{24} = \frac{1}{3} \cdot \left(- \frac{7}{15}\right) + c$

$c = - \frac{5}{24} + \frac{1}{3} \cdot \frac{7}{15}$

$c = - \frac{19}{360}$

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Let the desired equation be

$y = m x + c$
To find out $c$, insert values of the $m , x \mathmr{and} y$ coordinates from the given point.
$- \frac{5}{24} = \left(\frac{1}{3}\right) \cdot \left(- \frac{7}{15}\right) + c$

$\implies c = - \frac{5}{24} + \frac{1}{3} \cdot \frac{7}{15}$

$\implies c = - \frac{5}{24} + \frac{7}{45}$
$\implies c = \frac{- 5 \cdot 15 + 7 \cdot 8}{360}$
$\implies c = \frac{- 75 + 56}{360}$
$\implies c = - \frac{19}{360}$

Feb 14, 2016

$y = \frac{1}{3} x - \frac{19}{360}$

#### Explanation:

The first answer is correct, but I would like to provide an alternative solution using the point-slope form.

Point-slope form:

Given a point $\left({x}_{0} , {y}_{0}\right)$ and a slope $m$, the equation of the line is:

$\text{ } y - {y}_{0} = m \left(x - {x}_{0}\right)$

You just have to substitute everything.

Solution

$\left[1\right] \text{ } y - {y}_{0} = m \left(x - {x}_{0}\right)$

$\left[2\right] \text{ } y + \frac{5}{24} = \frac{1}{3} \left(x + \frac{7}{15}\right)$

$\left[3\right] \text{ } y + \frac{5}{24} = \frac{1}{3} x + \frac{7}{45}$

$\left[4\right] \text{ } y = \frac{1}{3} x + \frac{7}{45} - \frac{5}{24}$

$\left[5\right] \text{ } y = \frac{1}{3} x + \frac{7}{45} - \frac{5}{24}$

$\left[6\right] \text{ } y = \frac{1}{3} x + \frac{56 - 75}{360}$

$\left[7\right] \text{ } \textcolor{b l u e}{y = \frac{1}{3} x - \frac{19}{360}}$