Answer:
(10, 4) which is the third option
Step-by-step explanation:
The given inequality is
[tex]y \le \dfrac{2}{5}x + 1[/tex]
To test if a point (x', y') satisfies this inequality, plug in the value of x' in the expression on the right and see if y' is indeed less than or equal to the result on the right
Let's plug in each value pair from the answer choices
First option: (10, 5.5)
Plug in these values for y on the left and x on the right
[tex]\: 5.5 \le \dfrac{2}{5}(10) + 1 \:?\\\\5.5 \le 4 + 1 \: ?\\\\5.5 \le 5 \: ?\\[/tex]
NO! Eliminate first option
Second option (-10, 6)
[tex]\: 6 \le \dfrac{2}{5}(-10) + 1 \:?\\\\6 \le -4 + 1 \: ?\\\\6 \le 3 \: ?\\[/tex]
NO! Eliminate second option
Third option (10, 4)
[tex]\: 4 \le \dfrac{2}{5}(10) + 1 \:?\\\\4 \le 4 + 1 \: ?\\\\4 \le 5 \: ?\\[/tex]
YES!
Since there is only one answer choice we need not check the last option values
Correct answer: (10, 4) which is option 3
Side note(not necessary but informative)
There is a more intelligent way of working this out. Since the x value is either 10 or -10, the first term (2/5)x will either be -4 or + 4
Right side will be -4 + 1 or +4 + 1 depending on the sign of 10
So right side will be either 3 (for x = -10) or 5 (for x = 10)
so we can compare option values as follows starting from the top:
For (10, 5.5) ==> 5.5 ≤ 5 ?
(-10, 6) ==> 6 ≤ 3?
(10, 4) ==> 4 ≤ 5
(10, 6) ==> 6 ≤ 5 ?
