To determine which points are solutions to the inequality y < 5x + 2, we can substitute the x and y values of each point into the inequality.
The inequality describes a region where the y-value is less than the value of 5x + 2. This means that for each point (x, y), if we find that substituting these values into the inequality holds true, then that point is a solution.
Let’s take some example points to check:
- For the point (0, 0):
- Substituting into the inequality: 0 < 5(0) + 2, which simplifies to 0 < 2. This is true.
- For the point (1, 3):
- Substituting into the inequality: 3 < 5(1) + 2, which simplifies to 3 < 7. This is true.
- For the point (2, 12):
- Substituting into the inequality: 12 < 5(2) + 2, which simplifies to 12 < 12. This is false.
- For the point (1, 6):
- Substituting into the inequality: 6 < 5(1) + 2, which simplifies to 6 < 7. This is true.
In conclusion, the points (0, 0), (1, 3), and (1, 6) are solutions to the inequality y < 5x + 2, while the point (2, 12) is not. To identify other potential solutions, you can repeat this process with any other points you’re interested in.