Show which of the following points is part of the solution set for the inequality y≤25x+1

Question

.(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)

Answer 1

To determine which of the given points is part of the solution set for the inequality \( y \leq 25x + 1 \), we can substitute the \( x \) values of the points into the equation \( y = 25x + 1 \) and check whether the corresponding \( y \) values are less than or equal to the calculated \( y \) values from the equation.

1. Point \((-10, 6)\): \[ y = 25(-10) + 1 = -250 + 1 = -249 \] Check: \( 6 \leq -249 \) (false)

2. Point \((10, 4)\): \[ y = 25(10) + 1 = 250 + 1 = 251 \] Check: \( 4 \leq 251 \) (true)

3. Point \((10, 5.5)\): \[ y = 25(10) + 1 = 250 + 1 = 251 \] Check: \( 5.5 \leq 251 \) (true)

4. Point \((10, 6)\): \[ y = 25(10) + 1 = 250 + 1 = 251 \] Check: \( 6 \leq 251 \) (true)

Now, we see that points \((10, 4)\), \((10, 5.5)\), and \((10, 6)\) are all valid solutions as they satisfy the inequality. However, only one point is needed:

So, the points \((10, 4)\), \((10, 5.5)\), and \((10, 6)\) are part of the solution set for the inequality \( y \leq 25x + 1 \). If you must choose only one, you can select any of these three as a correct answer, for example, \((10, 4)\).