College Algebra, Chapter 3, 3.2, Section 3.2, Problem 76

Find a function whose graph is the line segment joining the points $(-3, -2)$ and $(6, 3)$

Using Two-Point Form


$
\begin{equation}
\begin{aligned}

y - y_1 =& \left( \frac{y_2 - y_1}{x_2 - x_1} \right) (x - x_1)
&&
\\
\\
y - (-2) =& \left[ \frac{3 - (-2)}{6 - (-3)} \right] [x - (-3)]
&& \text{Substitute } x_1 = -3, x_2 = 6 \text{ and } y_1 = -2, y_2 = 3
\\
\\
y + 2 =& \left( \frac{3 + 2}{6 + 3} \right) (x + 3)
&& \text{Simplify}
\\
\\
y + 2 =& \frac{5}{9} (x + 3)
&& \text{Subtract } 2
\\
\\
y =& \frac{5}{9} (x + 3) - 2
&& \text{Apply Distributive Property}
\\
\\
y =& \frac{5x + 15}{9} - 2
&& \text{Get the LCD}
\\
\\
y =& \frac{5x + 15 - 18}{9}
&& \text{Simplify}
\\
\\
y =& \frac{5x - 3}{9}
&& \text{Answer}


\end{aligned}
\end{equation}
$