6. Which of these points would be in the solution set of y < 2x – 5? The points would be in the shaded region of the graph:
(2, -1) (7, 100) (100, 7) (0 , 0)
It would be shaded under the line.
(0,0) is not true. 0< -5
(100,7) is true. 7< 195
(7,100) is not true. 100<9
(2,-1) is not true. -1<-1 <----(This would be true if it was less than or equal to sign.)
I should have know this. Over my head there for a minute. Thanks John!
To determine which points would be in the solution set of the inequality y < 2x - 5, we need to substitute the coordinates of each point into the inequality and check if it is satisfied.
Let's start by substituting the coordinates of the point (2, -1) into the inequality:
-1 < 2(2) - 5
-1 < 4 - 5
-1 < -1
Since -1 is less than -1, the point (2, -1) satisfies the inequality.
Now let's test the point (7, 100):
100 < 2(7) - 5
100 < 14 - 5
100 < 9
Since 100 is not less than 9, the point (7, 100) does not satisfy the inequality.
Next, let's test the point (100, 7):
7 < 2(100) - 5
7 < 200 - 5
7 < 195
Since 7 is less than 195, the point (100, 7) satisfies the inequality.
Lastly, let's test the point (0, 0):
0 < 2(0) - 5
0 < 0 - 5
0 < -5
Since 0 is not less than -5, the point (0, 0) does not satisfy the inequality.
Therefore, the points that would be in the solution set of y < 2x - 5 are:
(2, -1) and (100, 7).