Algebra - Lines

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Section 3.2 : Lines

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7. Determine the slope of the line and sketch the graph of the following line.

$5x - 2y = 6$

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The first thing that we should do here is write the equation of the line in slope-intercept form. This will help with both finding the slope and with sketching the graph.

Here is the slope-intercept form of the line.

$\begin{align*}5x - 2y & = 6\\ 5x & = 2y + 6\\ 5x - 6 & = 2y\hspace{0.25in} \Rightarrow \hspace{0.25in}y = \frac{5}{2}x - 3\end{align*}$ Show Step 2

From the equation of the line in slope-intercept form that we found in the previous step we see that the slope is : $\require{bbox} \bbox[2pt,border:1px solid black]{{\frac{5}{2}}}$ .

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From the equation of line in slope-intercept form that we found in Step 1 we see that the $y$ -intercept from of the line is $\left( {0, - 3} \right)$ . Also, from the slope we found in Step 2 we know that the “rise” is 5 and the “run” is 2 and so a second point on the graph of the line is,

${x_2} = 0 + 2 + 2\hspace{0.25in}\hspace{0.25in}{y_2} = - 3 + 5 = 2\hspace{0.25in}\hspace{0.25in} \Rightarrow \hspace{0.25in}\left( {2,2} \right)$

Using these two points we can sketch the graph of the line.