18x2 + 4 – [6(x2 – 2) + 5]
1 answer:
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Answer: see image attached
y<x/2+6 is the yellowish area (with dashed boundary as that does not belong to the solution space)
x+3y>=12 is rearranged as y>=-x/3+4 and solutions correspond to the bluish shaded area (with solid line, due to the equal sign)
The solutions satisfying both inequalities are in the overlap area of the two.
For this case we have the following equation:
That can be rewritten in the form
Where:
- m is the slope of the line
- b is the cut point
So, we have:
Where:
is the slope
is the cut point
Carlota has the following points:
(-1, 3) and (2, 9)
To know if the line passes through these points, we must replace them in the equation and the equality must be fulfilled. So:
Point (-1, 3):
Substituting:
It's false, equality is not met. The point (-1, 3) does not go through the line.
The equation written by Carlota is erroneous, the procedure to follow is:
Given and
, we find the slope:
We observe that the slope found by Carlota is the same. Let's see cut point "b". For this we substitute any of the points given in the equation:
Substituting (2,9) we have:
Thus, Carlota's error was at the cut-off point. The correct equation of the line that passes through the given points is
Answer:
The correct equation of the line that passes through the given points is
Carlota's mistake was at the cutoff point