Graph:
y<2x
Pretend that the inequality is an equals sign, so y = 2x. This is a line with slope of +2, and it's x and y intercepts at the origin.
Now we want y to be less than 2x. This is represented as the area above / right of the line. To prove this to yourself, you could always test some points out. For example, the point (1, 0) is right of the line and plugging it in yields 0 < 2.
Since the inequality is strictly less than, the line should be dotted, so we retroactively erase part of the line. (Less than or equal to would yield a solid line.)
while in this case, the explanation gives the right area, technically, the area to the right of the line is
x > y/2
Since the y-coordinates are measured vertically, you should be looking for the area below the line. In this case, it's the same area.
To graph the inequality y < 2x, follow these steps:
1. Start by graphing the line y = 2x.
- Choose several x-values and substitute them into the equation to find the corresponding y-values.
- For example, when x = 0, y = 2(0) = 0. This gives you the point (0, 0).
- Another point can be found by letting x = 1: y = 2(1) = 2. This gives you the point (1, 2).
- Connect these points with a straight line.
2. Determine the shading.
- Since the inequality is y < 2x, the shaded region is below the line y = 2x.
- You can shade the region below the line by making the line dashed, indicating that it is not included in the solution.
- Shade the area below the line with diagonal lines.
That's it! You have successfully graphed the inequality y < 2x.