How do you write an equation of a line with point (-4,6), slope -2?

Jun 25, 2018

See a solution process below:

Explanation:

We can use the point-slope formula to write an equation for this line. The point-slope form of a linear equation is: $\left(y - \textcolor{b l u e}{{y}_{1}}\right) = \textcolor{red}{m} \left(x - \textcolor{b l u e}{{x}_{1}}\right)$

Where $\left(\textcolor{b l u e}{{x}_{1}} , \textcolor{b l u e}{{y}_{1}}\right)$ is a point on the line and $\textcolor{red}{m}$ is the slope.

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

$\left(y - \textcolor{b l u e}{6}\right) = \textcolor{red}{- 2} \left(x - \textcolor{b l u e}{- 4}\right)$

$\left(y - \textcolor{b l u e}{6}\right) = \textcolor{red}{- 2} \left(x + \textcolor{b l u e}{4}\right)$

We can also solve for $y$ to put the equation 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.

$y - \textcolor{b l u e}{6} = \left(\textcolor{red}{- 2} \times x\right) + \left(\textcolor{red}{- 2} \times \textcolor{b l u e}{4}\right)$

$y - \textcolor{b l u e}{6} = \textcolor{red}{- 2} x + \left(- 8\right)$

$y - \textcolor{b l u e}{6} = \textcolor{red}{- 2} x - 8$

$y - \textcolor{b l u e}{6} + \textcolor{b l u e}{6} = \textcolor{red}{- 2} x - 8 + \textcolor{b l u e}{6}$

$y - 0 = \textcolor{red}{- 2} x - \textcolor{b l u e}{2}$

$y = \textcolor{red}{- 2} x - \textcolor{b l u e}{2}$