What is the equation in point-slope form and slope intercept form for the line given slope= -1/2, (0,3)?

Mar 5, 2018

See a solution process below:

Explanation:

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 gives:

$\left(y - \textcolor{b l u e}{3}\right) = \textcolor{red}{- \frac{1}{2}} \left(x - \textcolor{b l u e}{0}\right)$

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.

$\left(0 , 3\right)$ is the same as having a $y$-intercept of $3$

Substituting gives:

$y = \textcolor{red}{- \frac{1}{2}} x + \textcolor{b l u e}{3}$