Beginning Algebra With Applications, Chapter 5, 5.3, Section 5.3, Problem 44

Graph $\displaystyle y = \frac{3}{4} x + 1$ by using the slope and $y$-intercept.

$y$-intercept:


$\begin{equation} \begin{aligned} y =& \frac{3}{4} x + 1 && \text{Given equation} \\ y =& \frac{3}{4} (0) + 1 && \text{To find the $y$-intercept, let } x = 0 \\ y =& 1 && \end{aligned} \end{equation}$


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


$\begin{equation} \begin{aligned} m =& \frac{\text{change in } y}{\text{change in } x} \\ \\ m =& \frac{3}{4} \end{aligned} \end{equation}$


Beginning at the $y$-intercept, move to the right 4 units and then up 3 units.







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

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