# What is the equation of the line with slope  m= 14/25  that passes through  (12/5 29/10) ?

Jul 30, 2017

See a solution process below:

#### Explanation:

Point Slope Solution
We can use the point slope formula to write and equation for this line. The point-slope formula states: $\left(y - \textcolor{red}{{y}_{1}}\right) = \textcolor{b l u e}{m} \left(x - \textcolor{red}{{x}_{1}}\right)$

Where $\textcolor{b l u e}{m}$ is the slope and $\left(\textcolor{red}{{x}_{1} , {y}_{1}}\right)$ is a point the line passes through.

Substituting the slope and values from the point in the problem gives:

$\left(y - \textcolor{red}{\frac{29}{10}}\right) = \textcolor{b l u e}{\frac{14}{25}} \left(x - \textcolor{red}{\frac{12}{5}}\right)$

Slope-Intercept Solution
We can also use the slope-intercept formula to write and equation for the line. The slope-intercept form of a linear equation is: $y = \textcolor{red}{m} x + \textcolor{b l u e}{b}$

Where $\textcolor{red}{m}$ is the slope and $\textcolor{b l u e}{b}$ is the y-intercept value.

We can substitute the slope from the problem for $\textcolor{red}{m}$ and the values from the point in the problem for $x$ and $y$ and solve for $\textcolor{b l u e}{b}$:

$\frac{29}{10} = \left(\textcolor{red}{\frac{14}{25}} \cdot \frac{12}{5}\right) + \textcolor{b l u e}{b}$

$\frac{29}{10} = \frac{168}{125} + \textcolor{b l u e}{b}$

$\frac{29}{10} - \textcolor{red}{\frac{168}{125}} = \frac{168}{125} - \textcolor{red}{\frac{168}{125}} + \textcolor{b l u e}{b}$

$\left(\frac{25}{25} \times \frac{29}{10}\right) - \left(\frac{2}{2} \times \textcolor{red}{\frac{168}{125}}\right) = 0 + \textcolor{b l u e}{b}$

$\frac{725}{250} - \frac{336}{250} = 0 + \textcolor{b l u e}{b}$

$\frac{389}{250} = \textcolor{b l u e}{b}$

Substituting the slope from the problem and the $y$-intercept we calculated into the formula gives:

$y = \textcolor{red}{\frac{14}{25}} x + \textcolor{b l u e}{\frac{389}{250}}$