Tuesday, September 4, 2012

Beginning Algebra With Applications, Chapter 5, 5.4, Section 5.4, Problem 26

Using the point slope formula, find the equation of the line that passes through the point whose coordinates are $(3,-1)$ and has slope of $\displaystyle \frac{2}{3}$


$
\begin{equation}
\begin{aligned}

(x_1, y_1) =& (3,-1)
&& \text{Let $(x_1, y_1)$ be the given point}
\\
m =& \frac{2}{3}
&& \text{$m$ is the given slope}
\\
y - y_1 =& m(x- x_1)
&& \text{Point slope formula}
\\
y - (-1) =& \frac{2}{3} (x-3)
&& \text{Substitute $3$ for $x$, $-1$ for $y$ and } \frac{2}{3} \text{ for $m$}
\\
y + 1 =& \frac{2}{3} x - 2
&& \text{Rewrite the equation in the form } y = mx+b
\\
y =& \frac{2}{3}x - 3
&& \text{Add $-1$}

\end{aligned}
\end{equation}
$

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