Question

Which point is located on the line represented by the equation y-5=2/3(x+9)

the answers are (2/3,5) (9,-5) (5,-9) (-9,5) (-5,9)

Answer 1

[AI-generated answer — Bot GPT 3.5]

To determine which point is located on the line, we need to substitute the x and y coordinates from each answer choice into the equation and see if they satisfy the equation.

Let's substitute the coordinates from each answer choice into the equation:

1) (2/3, 5)
If we substitute x = 2/3 and y = 5 into the equation, we get:
5 - 5 = (2/3)(2/3 + 9)
0 = 2/3(19/3)
0 = 38/9
Since 0 is not equal to 38/9, this point is not on the line.

2) (9, -5)
If we substitute x = 9 and y = -5 into the equation, we get:
-5 - 5 = (2/3)(9 + 9)
-10 = 2/3(18)
-10 = 12
Since -10 is not equal to 12, this point is not on the line.

3) (5, -9)
If we substitute x = 5 and y = -9 into the equation, we get:
-9 - 5 = (2/3)(5 + 9)
-14 = 2/3(14)
-14 = 28/3
Since -14 is not equal to 28/3, this point is not on the line.

4) (-9, 5)
If we substitute x = -9 and y = 5 into the equation, we get:
5 - 5 = (2/3)(-9 + 9)
0 = 2/3(0)
0 = 0
Since 0 is equal to 0, this point is on the line.

5) (-5, 9)
If we substitute x = -5 and y = 9 into the equation, we get:
9 - 5 = (2/3)(-5 + 9)
4 = 2/3(4)
4 = 8/3
Since 4 is not equal to 8/3, this point is not on the line.

Thus, the point (-9, 5) is the only point that is located on the line represented by the equation y - 5 = (2/3)(x + 9).