Question

Show which of the following points is part of the solution set for the inequality y≤25x+1 .(1 point) Responses (−10,6) left parenthesis negative 10 comma 6 right parenthesis (10,4) left parenthesis 10 comma 4 right parenthesis (10,5.5) left parenthesis 10 comma 5.5 right parenthesis (10,6) left parenthesis 10 comma 6 right parenthesis

Answer 1

To determine which points are part of the solution set for the inequality \( y \leq 25x + 1 \), we can substitute the x-values of each point into the equation and check if the corresponding y-value meets the condition of the inequality.

1. For the point \((-10, 6)\): \[ y = 6 \quad \text{and} \quad x = -10 \] Substitute into the inequality: \[ 6 \leq 25(-10) + 1 \quad \Rightarrow \quad 6 \leq -250 + 1 \quad \Rightarrow \quad 6 \leq -249 \quad \text{(False)} \]

2. For the point \((10, 4)\): \[ y = 4 \quad \text{and} \quad x = 10 \] Substitute into the inequality: \[ 4 \leq 25(10) + 1 \quad \Rightarrow \quad 4 \leq 250 + 1 \quad \Rightarrow \quad 4 \leq 251 \quad \text{(True)} \]

3. For the point \((10, 5.5)\): \[ y = 5.5 \quad \text{and} \quad x = 10 \] Substitute into the inequality: \[ 5.5 \leq 25(10) + 1 \quad \Rightarrow \quad 5.5 \leq 250 + 1 \quad \Rightarrow \quad 5.5 \leq 251 \quad \text{(True)} \]

4. For the point \((10, 6)\): \[ y = 6 \quad \text{and} \quad x = 10 \] Substitute into the inequality: \[ 6 \leq 25(10) + 1 \quad \Rightarrow \quad 6 \leq 250 + 1 \quad \Rightarrow \quad 6 \leq 251 \quad \text{(True)} \]

From the analysis above:

• The point \((-10, 6)\) is not part of the solution set.
• The points \((10, 4)\), \((10, 5.5)\), and \((10, 6)\) are part of the solution set.

Thus, the points that are part of the solution set for the inequality are \((10, 4)\), \((10, 5.5)\), and \((10, 6)\).