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 (10,5.5) left parenthesis 10 comma 5.5 right parenthesis (10,6) left parenthesis 10 comma 6 right parenthesis (10,4)

Answer 1

To determine which of the given points is part of the solution set for the inequality $y\le 25x+1$, we will substitute the x and y coordinates of each point into the inequality and check if it holds true.

1. For the point $(-10,6)$: $$y\le 25x+1⟹6\le 25(-10)+1⟹6\le -250+1⟹6\le -249\text{(False)}$$

2. For the point $(10,5.5)$: $$y\le 25x+1⟹5.5\le 25(10)+1⟹5.5\le 250+1⟹5.5\le 251\text{(True)}$$

3. For the point $(10,6)$: $$y\le 25x+1⟹6\le 25(10)+1⟹6\le 250+1⟹6\le 251\text{(True)}$$

4. For the point $(10,4)$: $$y\le 25x+1⟹4\le 25(10)+1⟹4\le 250+1⟹4\le 251\text{(True)}$$

Thus, the points $(10,5.5)$, $(10,6)$, and $(10,4)$ are all part of the solution set for the inequality, while $(-10,6)$ is not.

Therefore, the points that are part of the solution set are:

• $(10,5.5)$
• $(10,6)$
• $(10,4)$