# How do you write an equation of a line with point (6,4), slope -3/4?

Feb 10, 2017

$\left(y - \textcolor{red}{4}\right) = \textcolor{b l u e}{- \frac{3}{4}} \left(x - \textcolor{red}{6}\right)$

Or

$y = \textcolor{red}{- \frac{3}{4}} x + \textcolor{b l u e}{\frac{34}{4}}$

#### Explanation:

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 point and the slope from the problem gives:

$\left(y - \textcolor{red}{4}\right) = \textcolor{b l u e}{- \frac{3}{4}} \left(x - \textcolor{red}{6}\right)$

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 solve the equation above for $y$ to put it into this form.

$y - \textcolor{red}{4} = \left(\textcolor{b l u e}{- \frac{3}{4}} \times x\right) - \left(\textcolor{b l u e}{- \frac{3}{4}} \times \textcolor{red}{6}\right)$

$y - \textcolor{red}{4} = - \frac{3}{4} x + \frac{18}{4}$

$y - \textcolor{red}{4} + 4 = - \frac{3}{4} x + \frac{18}{4} + 4$

$y - 0 = - \frac{3}{4} x + \frac{18}{4} + \left(\frac{4}{4} \times 4\right)$

$y = - \frac{3}{4} x + \frac{18}{4} + \frac{16}{4}$

$y = - \frac{3}{4} x + \frac{34}{4}$