# What is the equation of the line with slope  m= 7/25  that passes through  (47/5 32/10) ?

Jan 20, 2016

$y = \frac{7}{25} x + \frac{71}{125}$

#### Explanation:

Given:

P_1(x_1;y_1)

The equation of a line through a point is:

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

$\therefore y - \frac{32}{10} = \frac{7}{25} \cdot \left(x - \frac{47}{5}\right)$

$y = \frac{7}{25} x - \frac{329}{125} + {\textcolor{g r e e n}{\cancel{32}}}^{\textcolor{g r e e n}{16}} / {\textcolor{g r e e n}{\cancel{10}}}^{\textcolor{g r e e n}{5}}$

$y = \frac{7}{25} x + \frac{- 329 + 400}{125}$

$y = \frac{7}{25} x + \frac{71}{125}$

Jan 20, 2016

The equation in slope-intercept form is $y = \frac{7}{25} x + \frac{71}{125}$.

#### Explanation:

We can use the slope-intercept form of a straight line, $y = m x + b$, where slope, $m$ is $\frac{7}{25}$, $x = \frac{47}{5}$, and $y = \frac{32}{10}$.

Notice that we don't know the y-intercept, $b$. Rearrange the equation to isolate $b$, substitute the given values and solve.

$y = m x + b$

$b = y - m x$

$b = \frac{32}{10} - \left(\frac{7}{25}\right) \left(\frac{47}{5}\right)$

Simplify.

$b = \frac{32}{10} - \frac{329}{125}$

Simplify $\frac{32}{10}$ to $\frac{16}{5}$.

$b = \frac{16}{5} - \frac{329}{125}$

The LCD is $125$. Multiply $\frac{16}{5}$ times $\frac{25}{25}$.

$b = \frac{16}{5} \left(\frac{25}{25}\right) - \frac{329}{125}$

Simplify.

$b = \frac{400}{125} - \frac{329}{125}$

Simplify.

$b = \frac{71}{125}$

The equation in slope-intercept form is $y = \frac{7}{25} x + \frac{71}{125}$.