Question
Use the image to answer the question.
Four points and two intersecting lines are plotted on a coordinate plane. The x-axis ranges from negative 15 to 15 in unit increments, labeled at every 5. The y-axis ranges from negative 10 to 10 in unit increments, labeled at every 5.
Which of the points on the graph is a solution to the simultaneous inequalities y≤14x+2 and y>12x+3 ? Enter the x-value followed by the y-value.
(1 point)
Four points and two intersecting lines are plotted on a coordinate plane. The x-axis ranges from negative 15 to 15 in unit increments, labeled at every 5. The y-axis ranges from negative 10 to 10 in unit increments, labeled at every 5.
Which of the points on the graph is a solution to the simultaneous inequalities y≤14x+2 and y>12x+3 ? Enter the x-value followed by the y-value.
(1 point)
Answers
There are no human answers yet.
Answered by
GPT-4o mini
To determine which point satisfies the inequalities \( y \leq 14x + 2 \) and \( y > 12x + 3 \), we need to evaluate each point based on these criteria.
1. **Identify the lines from the inequalities:**
- The line \( y = 14x + 2 \) is the boundary for the first inequality. Points below this line will satisfy \( y \leq 14x + 2 \).
- The line \( y = 12x + 3 \) is the boundary for the second inequality. Points above this line will satisfy \( y > 12x + 3 \).
2. **Substitute the x-values of each point to find corresponding y-values.**
- For each point, we will determine if it lies below the first line and above the second line to see which inequalities it satisfies.
3. **Select candidate points and perform the checks (hypothetically, let’s say you have candidate points):**
- For point \( P_1(a, b) \):
- Check if \( b \leq 14a + 2 \)
- Check if \( b > 12a + 3 \)
Continue this for all plotted points.
4. **Once the calculations are complete**, the point that meets both criteria will be the solution.
If you have a specific set of points from your image, please provide those points, and I can help you determine which one is a solution to the inequalities!
1. **Identify the lines from the inequalities:**
- The line \( y = 14x + 2 \) is the boundary for the first inequality. Points below this line will satisfy \( y \leq 14x + 2 \).
- The line \( y = 12x + 3 \) is the boundary for the second inequality. Points above this line will satisfy \( y > 12x + 3 \).
2. **Substitute the x-values of each point to find corresponding y-values.**
- For each point, we will determine if it lies below the first line and above the second line to see which inequalities it satisfies.
3. **Select candidate points and perform the checks (hypothetically, let’s say you have candidate points):**
- For point \( P_1(a, b) \):
- Check if \( b \leq 14a + 2 \)
- Check if \( b > 12a + 3 \)
Continue this for all plotted points.
4. **Once the calculations are complete**, the point that meets both criteria will be the solution.
If you have a specific set of points from your image, please provide those points, and I can help you determine which one is a solution to the inequalities!
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