How do you write an equation of a line given point (4,-6) and m=1?

Jul 22, 2017

See a solution process below:

Explanation:

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

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

$\left(y - \textcolor{red}{- 6}\right) = \textcolor{b l u e}{1} \left(x - \textcolor{red}{4}\right)$

$\left(y + \textcolor{red}{6}\right) = \textcolor{b l u e}{1} \left(x - \textcolor{red}{4}\right)$

If necessary, we can convert this equation to slope-intercept by solving for $y$. 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.

$y + \textcolor{red}{6} = x - \textcolor{red}{4}$

$y + \textcolor{red}{6} - 6 = x - \textcolor{red}{4} - 6$

$y + 0 = x - 10$

$y = \textcolor{red}{1} x - \textcolor{b l u e}{10}$