Precalculus, Chapter 1, 1.3, Section 1.3, Problem 108

Find the equation of the line whose graph is given.







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



$\displaystyle m = \frac{1-0}{0-1} = \frac{1}{-1} = -1$



The slope is $-1$. 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 =& -1(x-1)
&& \text{Substitute $m = -1, x = 1$ and $y = 0$}
\\
y =& -x + 1
&& \text{Slope Intercept Form}
\\
\text{or} &
&&
\\
x + y =& 1
&& \text{General Form}

\end{aligned}
\end{equation}
$