Beginning Algebra With Applications, Chapter 5, 5.3, Section 5.3, Problem 46

Graph $\displaystyle 3x-y = 1$ by using the slope and $y$-intercept.

$y$-intercept:


$
\begin{equation}
\begin{aligned}

3x-y =& 1
&& \text{Given equation}
\\
3(0) - y =& 1
&& \text{To find the $y$-intercept, let } x = 0
\\
-y =& 1
&& \text{Simplify}
\\
y =& -1
&&

\end{aligned}
\end{equation}
$


The $y$-intercept is $(0,-1)$


$
\begin{equation}
\begin{aligned}

m =& \frac{\text{change in } y}{\text{change in } x}
\\
\\
m =& \frac{3}{1}

\end{aligned}
\end{equation}
$


Beginning at the $y$-intercept, move to the right 1 unit and then up 3 units.







$(1, 2)$ are the coordinates of a second point on the graph.

Draw a line through $(0,-1)$ and $(1, 2)$