Section 3.2 : Lines
7. Determine the slope of the line and sketch the graph of the following line.
\[5x - 2y = 6\]Show All Steps Hide All Steps
Start SolutionThe 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 2From the equation of the line in slope-intercept form that we found in the previous step we see that the slope is : \(\require{bbox} \bbox[2pt,border:1px solid black]{{\frac{5}{2}}}\) .
Show Step 3From 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.
