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

(10,6)
left parenthesis 10 comma 6 right parenthesis

(10,5.5)
left parenthesis 10 comma 5.5 right parenthesis

(10,4)

1 answer

To determine which points are part of the solution set for the inequality \(y \leq 25x + 1\), we need to check each point by substituting the \(x\) value into the inequality and comparing the \(y\) value.

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

  2. For the point \((10, 6)\): \[ y \leq 25(10) + 1 \Rightarrow 6 \leq 250 + 1 \Rightarrow 6 \leq 251 \quad \text{(True)} \]

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

  4. For the point \((10, 4)\): \[ y \leq 25(10) + 1 \Rightarrow 4 \leq 250 + 1 \Rightarrow 4 \leq 251 \quad \text{(True)} \]

Therefore, the points \((10, 6)\), \((10, 5.5)\), and \((10, 4)\) are all part of the solution set for the inequality \(y \leq 25x + 1\).

The correct answer(s) are:

  • \((10, 6)\)
  • \((10, 5.5)\)
  • \((10, 4)\)

All of these points are valid solutions, but if you're only looking for one, you can choose any of them.