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 $(1, 2)$