SOLUTION: Is the inequality -x-4y>3 in the correct form for graphing? Explain

Question 632619: Is the inequality -x-4y>3 in the correct form for graphing? Explain
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
Not knowing your teacher, textbook and/or course materials, I do not know what the expected answer is. Personally, I believe the question reflects the wrong approach to teach math, and that only a student in your class could figure out what the expected answer is. However, I can venture a guess.

MY GUESS ABOUT THE EXPECTED ANSWER:
The inequality -x-4y>3 is not in the correct form for graphing.
We must have the equation in the slope-intercept form (y=mx+b) to graph it.
That way we can graph the boundary line and decide what side of the line corresponds to the solution of the problem.
So we transform the inequality in steps.
First, we add x to both sides, which does not alter the direction of the inequality sign:
-x-4y>3 --> -4y>x+3
Then we multiply both sides times (-1/4) (or divide both sides by (-4), same thing) and reverse the inequality sign, because we must reverse the sign when we multiply or divided by a negative number:
-4y>x+3 --> y<-(1/4)x-3/4
Then we draw a dashed line with slope -1/4 that goes through its y intercept at (0,-3/4).
The line must be dashed because the points on the line, where y=-(1/4)x-3/4 do not satisfy the inequality.
Finally, we color or shade the region of the graph that is below the line because the inequality refers to values of y that are "less than" the y for the points on the line.

WHY I DO NOT LIKE THAT ANSWER, OR THE QUESTION:
The question hints that there is only one correct procedure (that should be memorized) to solve this type of problem.
I do not believe anyone should have to memorize anything in math, beyond the definitions necessary to make sure we are all talking the same language. Feeding students procedures may be an easy way to help them do a little better in a test, but does not improve understanding.
Since the memorized procedure will soon be forgotten, I would not call that teaching/learning.
I can usually see several correct ways to approach and solve a problem, and believe that we should respect people who use a different correct approach, regardless of their age, or educational status.

HOW I WOULD SOLVE THE PROBLEM:
The boundary line is the graph of the equation -x-4y=3.
That line should be drawn dashed because the inequality does not include "equal to", only "greater than". For the solution to include points in the graph of -x-4y=3, The inequality would have to have "or equal" in its sign, as in
.
To graph -x-4y=3, I need 2 points from that line, and I can see two points that are easy enough to get from the equation as given.
When x=0, -0-4y=3 --> -4y=3 --> y=-3/4 gives me point (0,-3/4).
When y=0, -x-4*0=3 --> -x=3 --> x=-3 gives me point (-3,0).
I can now plot those two points and draw the line.
I made the line blue, and circled the points for visibility.
The graphed solution should have the region to one side of the line colored or shaded.
To find which side, I use a point that is not on the line as a test point.
In this case (and often) the origin (the point (0,0) with x=y=0) makes it easiest.
Substituting x=y=0 in -x-4y>3, I get
-0-4*0>3 or 0>3, which is not true, so I know that the origin is not part of the solution to the inequality,
and I color or shade the side of the line that does not contain the origin.
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