How do you find equation of line passing through the point P(8,2) with a slope of 4?

Apr 23, 2017

See the the entire solution process below:

Explanation:

We can use the point-slope formula to find an equation for the line described 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:

$\left(y - \textcolor{red}{2}\right) = \textcolor{b l u e}{4} \left(x - \textcolor{red}{8}\right)$

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

$y - \textcolor{red}{2} = \textcolor{b l u e}{4} \left(x - \textcolor{red}{8}\right)$

$y - \textcolor{red}{2} = \left(\textcolor{b l u e}{4} \cdot x\right) - \left(\textcolor{b l u e}{4} \cdot \textcolor{red}{8}\right)$

$y - \textcolor{red}{2} = 4 x - 32$

$y - \textcolor{red}{2} + 2 = 4 x - 32 + 2$

$y - 0 = 4 x - 30$

$y = \textcolor{red}{4} x - \textcolor{b l u e}{30}$