What is the equation of the line with slope  m= -1/25  that passes through  (7/5, 1/10) ?

Jun 25, 2016

In point slope form:

$y - \frac{1}{10} = - \frac{1}{25} \left(x - \frac{7}{5}\right)$

In slope intercept form:

$y = - \frac{1}{25} x + \frac{39}{250}$

Explanation:

Given a slope $m$ and a point $\left({x}_{1} , {y}_{1}\right)$ through which a line passes, its equation can be written in point slope form:

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

In our example, $m = - \frac{1}{25}$ and $\left({x}_{1} , {y}_{1}\right) = \left(\frac{7}{5} , \frac{1}{10}\right)$, so we get the equation:

$y - \frac{1}{10} = - \frac{1}{25} \left(x - \frac{7}{5}\right)$

Expanding and rearranging, this can be expressed as:

$y = - \frac{1}{25} x + \frac{39}{250}$

which is in slope intercept form:

$y = m x + b$

with $m = - \frac{1}{25}$ and $b = \frac{39}{250}$

graph{(y - 1/10 + 1/25(x-7/5))(x^2+(y-39/250)^2-0.0017)((x-7/5)^2+(y-1/10)^2-0.0017)=0 [-1.76, 3.24, -1.17, 1.33]}