Which is the graph of linear inequality x – 2y ≥ –12?
1 answer:
Answer:
option D
Step-by-step explanation:
x-2y≥-12
-2y≥-x-12
y≤0.5x+6
has to be a solid line since y is less than or equal to 0.5x+6
so, options 1 and 3 are not applicable
also, in y≤0.5x+6 , y is less than or equal to this line, thus it only exists on the line and to the right of it (below it)
so, option 2 is wrong also, leaving us with option 4 or D, which in this case is the answer
I attached a file of this inequality's graph to prove my answer once more
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General Idea:
When a point or figure on a coordinate plane is moved by sliding it to the right or left or up or down, the movement is called a translation.
Say a point P(x, y) moves up or down ' k ' units, then we can represent that transformation by adding or subtracting respectively 'k' unit to the y-coordinate of the point P.
In the same way if P(x, y) moves right or left ' h ' units, then we can represent that transformation by adding or subtracting respectively 'h' units to the x-coordinate.
P(x, y) becomes . We need to use ' + ' sign for 'up' or 'right' translation and use ' - ' sign for ' down' or 'left' translation.
Applying the concept:
The point A of Pre-image is (0, 0). And the point A' of image after translation is (5, 2). We can notice that all the points from the pre-image moves 'UP' 2 units and 'RIGHT' 5 units.
Conclusion:
The transformation that maps ABCD onto its image is translation given by (x + 5, y + 2),
In other words, we can say ABCD is translated 5 units RIGHT and 2 units UP to get to A'B'C'D'.