Show which of the following points is part of the solution set for the inequality y is less than or equal to 2/5x + 1.

Question

A: (-10 , 6)

B: ( 10, 4)

C: ( 10, 6)

D: ( 10, 5.5)

Answer 1

To determine which of the given points is part of the solution set for the inequality $y\le \frac{2}{5}x+1$, we can substitute the $x$ and $y$ values of each point into the inequality and check if it holds true.

The inequality is: $$y\le \frac{2}{5}x+1$$

Let's evaluate each point:

A: (-10, 6)
Substituting $x=-10$ and $y=6$: $$6\le \frac{2}{5}(-10)+1$$ $$6\le -4+1$$ $$6\le -3$$ (False)

B: (10, 4)
Substituting $x=10$ and $y=4$: $$4\le \frac{2}{5}(10)+1$$ $$4\le 4+1$$ $$4\le 5$$ (True)

C: (10, 6)
Substituting $x=10$ and $y=6$: $$6\le \frac{2}{5}(10)+1$$ $$6\le 4+1$$ $$6\le 5$$ (False)

D: (10, 5.5)
Substituting $x=10$ and $y=5.5$: $$5.5\le \frac{2}{5}(10)+1$$ $$5.5\le 4+1$$ $$5.5\le 5$$ (False)

After checking all options, we find that the only point that satisfies the inequality is:

B: (10, 4).