Beginning Algebra With Applications, Chapter 5, 5.3, Section 5.3, Problem 52

Graph $\displaystyle y = -x-3$ by using the slope and $y$-intercept.

$y$-intercept:


$
\begin{equation}
\begin{aligned}

y =& -x-3
&& \text{Given equation}
\\
y =& 0-3
&& \text{To find the $y$-intercept, let } x = 0
\\
y =& -3
&&

\end{aligned}
\end{equation}
$


The $y$-intercept is $(0,-3)$


$
\begin{equation}
\begin{aligned}

m =& \frac{\text{change in } y}{\text{change in } x}
\\
\\
m =& \frac{-1}{1}
\\
\\
m =& -1

\end{aligned}
\end{equation}
$


Beginning at the $y$-intercept, move to the right 1 unit and then down 1 unit.







$(1, -4)$ are the coordinates of a second point on the graph.

Draw a line through $(0,-3)$ and $(1, -4)$