Question
y≥2x graph the linear inequality
Answers
GPT 3.5
To graph the linear inequality y ≥ 2x, we can start by graphing the line y = 2x, which has a slope of 2 and passes through the origin (0,0).
First, plot the point (0,0) on the coordinate plane.
Next, since the inequality is y ≥ 2x, we know that the line itself is included in the solution. So, we can draw a solid line to represent y = 2x.
To determine which side of the line to shade, we can choose a test point not on the line. Let's use the point (0,1) as our test point.
When we substitute the coordinates (x = 0, y = 1) into the inequality y ≥ 2x, we get 1 ≥ 2(0), which simplifies to 1 ≥ 0. Since this inequality is true, we shade the side of the line that contains the test point (0,1).
The graph should show a solid line with shading above (or to the right, depending on how you prefer to display your graph) the line.
First, plot the point (0,0) on the coordinate plane.
Next, since the inequality is y ≥ 2x, we know that the line itself is included in the solution. So, we can draw a solid line to represent y = 2x.
To determine which side of the line to shade, we can choose a test point not on the line. Let's use the point (0,1) as our test point.
When we substitute the coordinates (x = 0, y = 1) into the inequality y ≥ 2x, we get 1 ≥ 2(0), which simplifies to 1 ≥ 0. Since this inequality is true, we shade the side of the line that contains the test point (0,1).
The graph should show a solid line with shading above (or to the right, depending on how you prefer to display your graph) the line.