Manipulate so that the equation is in the form y=mx+by=mx+b, where mm is the slope and bb is the yy-intercept.
First, to isolate the yy-term, subtract 3/2x32x from both sides.
-1/3y=-3/2x+7/3−13y=−32x+73
To isolate just yy, multiply both sides by -3−3.
y=9/2x-7y=92x−7
This means that the function has an intercept at (0,-7)(0,−7).
The slope is 9/292. Slope is also known as "rise over run", since it represents the change in yy-values over the change in xx-values.
Thus, the "rise" is 99 for every "run" of 22. This means that if you have the point (0,-7)(0,−7), you know that the point (0+2,-7+9)=>(2,2)(0+2,−7+9)⇒(2,2) is also on the line.
Graph (2,2)(2,2) and draw the line. If you wish, you can continue going up 99 units and right 22 units to draw in more points. You can also go down 99 units and left 22 units.
graph{3/2x-1/3y=7/3 [-28.47, 44.6, -15.8, 20.72]}
