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 $(4, 4)$