Finite Mathematics, Chapter 1, 1.1, Section 1.1, Problem 22

Determine a equation in slope intercept form (where possible) for the line that goes through
$\displaystyle \left( -2, \frac{3}{4} \right)$ and $\displaystyle \left( \frac{2}{3} , \frac{5}{2} \right)$
Let $\displaystyle (x_1 , y_1) = \left( -2, \frac{3}{4} \right)$ and $\displaystyle (x_2, y_2) = \left( \frac{2}{3} , \frac{5}{2} \right)$.
Then, by using two point form
$\displaystyle y - y_1 = \frac{y_2 - y_1}{x_2 - x_1} (x - x_1)$


$
\begin{equation}
\begin{aligned}
y - \frac{3}{4} &= \frac{\frac{5}{2} - \frac{3}{4}}{\frac{2}{3} - (-2) } ( x - (-2))\\
\\
y - \frac{3}{4} &= \frac{\frac{10-3}{4}}{\frac{2}{3}+ 2} (x + 2)\\
\\
y - \frac{3}{4} &= \frac{\frac{7}{4}}{\frac{8}{3}} ( x + 2)\\
\\
y - \frac{3}{4} &= \frac{21}{32} (x + 2)\\
\\
y - \frac{3}{4} &= \frac{21}{32}x + \frac{21}{16}\\
\\
y &= \frac{21}{32}x + \frac{33}{16}
\end{aligned}
\end{equation}
$

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