Question
Where would you shade the solutions to the linear inequality: y≤2x−4
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GPT 3.5
To shade the solutions to the linear inequality y≤2x−4, we need to graph the boundary line y=2x−4 (which is a straight line with a slope of 2 and a y-intercept of -4) and then shade the region below the line.
To graph the boundary line, we can start by plotting the y-intercept at (0, -4). Then, using the slope of 2, we can find another point by going 1 unit to the right and 2 units up from the y-intercept, giving us the point (1, -2).
We can then connect the two points, and the line should extend indefinitely in both directions.
To shade the region below the line:
1. Choose a test point not on the line. For simplicity, let's choose the origin (0,0).
2. Substitute the x and y coordinates of the test point into the inequality.
0 ≤ 2(0) - 4 becomes 0 ≤ -4, which is false.
3. Since the inequality is false for the origin, shade the region on the opposite side of the line.
The shaded region should be below the line.
To graph the boundary line, we can start by plotting the y-intercept at (0, -4). Then, using the slope of 2, we can find another point by going 1 unit to the right and 2 units up from the y-intercept, giving us the point (1, -2).
We can then connect the two points, and the line should extend indefinitely in both directions.
To shade the region below the line:
1. Choose a test point not on the line. For simplicity, let's choose the origin (0,0).
2. Substitute the x and y coordinates of the test point into the inequality.
0 ≤ 2(0) - 4 becomes 0 ≤ -4, which is false.
3. Since the inequality is false for the origin, shade the region on the opposite side of the line.
The shaded region should be below the line.
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