Intermediate Algebra, Chapter 3, Summary Exercises, Section Summary Exercises, Problem 8

Write an equation of the line "through $(-2,5)$ and parallel to the graph of $3x - y = 4$".

(a) In slope-intercept form

We write the equation $3x - y = 4$ in slope-intercept form. To find the slope


$
\begin{equation}
\begin{aligned}

3x - y =& 4
&& \text{Given equation}
\\
-y =& -3x + 4
&& \text{Subtract each side by $3x$}
\\
y =& 3x - 4
&& \text{Divide each side by $-1$}

\end{aligned}
\end{equation}
$



The slope is $3$. Using Point Slope Form, with point $(-2,5)$


$
\begin{equation}
\begin{aligned}

y - y_1 =& m(x - x_1)
&& \text{Point Slope Form}
\\
y - 5 =& 3 [x - (-2)]
&& \text{Substitute } x = -2, y = 5 \text{ and } m = 3
\\
y - 5 =& 3x + 6
&& \text{Distributive Property}
\\
y =& 3x + 11
&& \text{Slope Intercept Form}

\end{aligned}
\end{equation}
$



(b) In standard form


$
\begin{equation}
\begin{aligned}

& y = 3x + 11
&& \text{Slope Intercept Form}
\\
& -3x + y = 11
&& \text{Standard Form}

\end{aligned}
\end{equation}
$

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