# How do you write an equation of a line given point (3,3) and m=4/3?

Apr 30, 2017

See the solution process below:

#### 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 slope and values from the points in the problem gives:

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

We can solve for $y$ to transform the equation to 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.

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

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

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

$y - 0 = \frac{4}{3} x - 1$

$y = \textcolor{red}{\frac{4}{3}} x - \textcolor{b l u e}{1}$