Precalculus, Chapter 1, 1.3, Section 1.3, Problem 110

Find the equation of the line whose graph is given.







Based from the graph, the intercepts are $(-2,0)$ and $(0,-1)$. Using the formula for slope, $\displaystyle m = \frac{y_2 - y_1}{x_2 - x_1}$, we have



$\displaystyle m = \frac{-1-0}{0-(-2)} = \frac{-1}{2}$



The slope is $\displaystyle \frac{-1}{2}$. Now we use point slope form to find the equation




$
\begin{equation}
\begin{aligned}

y - y_1 =& m(x - x_1)
&& \text{Point Slope Form}
\\
y - 0 =& \frac{-1}{2} [x - (-2)]
&& \text{Substitute } m = \frac{-1}{2}, x = -2 \text{ and } y = 0
\\
y =& \frac{-1}{2} x - 1
&& \text{Slope Intercept Form}
\\
\text{or} &
&&
\\
\frac{1}{2} x + y =& -1
&& \text{General Form}

\end{aligned}
\end{equation}
$