Section 3.2 : Lines
7. Determine the slope of the line and sketch the graph of the following line.
5x−2y=6Show 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.
5x−2y=65x=2y+65x−6=2y⇒y=52x−3 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 : 52 .
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 (0,−3) . 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,
x2=0+2+2y2=−3+5=2⇒(2,2)Using these two points we can sketch the graph of the line.
