Algebra - Lines

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Section 3.2 : Lines

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

$4y + x = 8$

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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.

$4y = - x + 8\hspace{0.25in}\hspace{0.25in} \Rightarrow \hspace{0.25in}\hspace{0.25in}y = - \frac{1}{4}x + 2$ 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 : $\require{bbox} \bbox[2pt,border:1px solid black]{{ - \frac{1}{4}}}$ .

Show Step 3

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 $\left( {0,2} \right)$ . Also, from the slope we found in Step 2 we know that the “rise” is -1 and the “run” is 4 and so a second point on the graph of the line is,

${x_2} = 0 + 4 = 4\hspace{0.25in}\hspace{0.25in}{y_2} = 2 + \left( { - 1} \right) = 1\hspace{0.25in} \Rightarrow \hspace{0.25in}\left( {4,1} \right)$

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