Precalculus, Chapter 1, 1.3, Section 1.3, Problem 48

Determine an equation for the line with a slope $\displaystyle \frac{1}{2}$ containing the point $(3,1)$. Express your answer using the general form or the slope intercept form of the equation of a line, which ever you prefer.

Using the Point Slope Form to find the equation


$
\begin{equation}
\begin{aligned}

y - y_1 =& m(x- x_1)
&& \text{Point Slope Form}
\\
\\
y - 1 =& \frac{1}{2} (x-3)
&& \text{Substitute } m = \frac{1}{2}, x = 3 \text{ and } y = 1
\\
\\
y =& \frac{1}{2}x - \frac{3}{2} + 1
&& \text{Simplify}
\\
y =& \frac{1}{2}x - \frac{1}{2}
&& \text{Slope Intercept Form}
\\
\text{or} &
&&
\\
\frac{1}{2}x - y =& \frac{1}{2}
&& \text{General Form}

\end{aligned}
\end{equation}
$