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Question 1209122: Please help me,how do I graph 3x-2y < 6 on a coordinate plane???
I simplified the equation to: y > 3/2x-3 but I'm not sure if I simplified it correctly.
Found 2 solutions by math_tutor2020, ikleyn:
Answer by math_tutor2020(3816)   (Show Source):
You can put this solution on YOUR website!
You solved for y correctly.
Consider the boundary equation y = (3/2)x - 3.
It's in slope-intercept form y = mx+b
m = 3/2 = slope
b = -3 = y intercept
Start at the anchor point (0,-3)
This is where the y intercept is located.
Move 3 units up and 2 units right. This movement pattern is due to the slope.
You should move from (0,-3) to (2,0)
Draw a straight line through those points. Extend the line as far as you can in either direction.
Make this a dashed line because there isn't an "or equal to" in the inequality sign for 3x-2y < 6.
A dashed line indicates points on the boundary are not in the solution set.
Now to the question: do we shade above the boundary? or below?
Since we have something of the form y > mx+b, it means we shade above.
The greater than symbol tells us this.
This rule only works if y is fully isolated or when the y coefficient is positive.
Another way to determine shading direction is to apply a test point like (x,y) = (0,0)
Make sure the test point is not on the boundary.
If so then move up or down 1 unit.
Luckily (0,0) isn't on the boundary.
Plug the test point into either inequality
3x-2y < 6
3*0-2*0 < 6
0 < 6
Or,
y > (3/2)*x - 3
0 > (3/2)*0 - 3
0 > -3
In either case, we get a true statement.
It proves that (0,0) is in the solution set.
Therefore, you shade the entire region containing (0,0).
This is proof we shade above the dashed boundary.
Graphing tools like Desmos and GeoGebra are useful to verify the answer.
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Recap:
Draw a dashed line through the points (0,-3) and (2,0)
Shade above the dashed line to complete the graph.
More practice with a similar question found here
Answer by ikleyn(52781)  (Show Source):
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