Use the image to answer the question.

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)

Answer 1

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!