# How do you write an equation in slope intercept form of a line containing the coordinates (2,5) with a slope of 3?

Mar 24, 2017

See the entire solution process below:

#### Explanation:

We can first 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:

$\left(y - \textcolor{red}{5}\right) = \textcolor{b l u e}{3} \left(x - \textcolor{red}{2}\right)$

Now, solve for $y$ to put the formula in 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.

$y - \textcolor{red}{5} = \left(\textcolor{b l u e}{3} \times x\right) - \left(\textcolor{b l u e}{3} \times \textcolor{red}{2}\right)$

$y - \textcolor{red}{5} = 3 x - 6$

$y - \textcolor{red}{5} + 5 = 3 x - 6 + 5$

$y - 0 = 3 x - 1$

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