What is the equation of the line with slope  m= 5/7  that passes through  (3/5,9/7) ?

1 Answer
May 8, 2017

See a solution process below:

Explanation:

We can use the point-slope formula to write an equation for the line in the problem. 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 $\textcolor{red}{\left(\left({x}_{1} , {y}_{1}\right)\right)}$ is a point the line passes through.

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

$\left(y - \textcolor{red}{\frac{9}{7}}\right) = \textcolor{b l u e}{\frac{5}{7}} \left(x - \textcolor{red}{\frac{3}{5}}\right)$

If required, we can solve for $y$ to put this equation in the slope-intercept form. 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.

$y - \textcolor{red}{\frac{9}{7}} = \left(\textcolor{b l u e}{\frac{5}{7}} \cdot x\right) - \left(\textcolor{b l u e}{\frac{5}{7}} \cdot \textcolor{red}{\frac{3}{5}}\right)$

$y - \textcolor{red}{\frac{9}{7}} = \frac{5}{7} x - \left(\textcolor{b l u e}{\frac{\textcolor{b l a c k}{\cancel{\textcolor{b l u e}{5}}}}{7}} \cdot \textcolor{red}{\frac{3}{\textcolor{b l a c k}{\cancel{\textcolor{red}{5}}}}}\right)$

$y - \textcolor{red}{\frac{9}{7}} = \frac{5}{7} x - \frac{3}{7}$

$y - \textcolor{red}{\frac{9}{7}} + \frac{9}{7} = \frac{5}{7} x - \frac{3}{7} + \frac{9}{7}$

$y - 0 = \frac{5}{7} x + \frac{6}{7}$

$y = \textcolor{red}{\frac{5}{7}} x + \textcolor{b l u e}{\frac{6}{7}}$