Which point is located on the line represented by the equation
y - 5 = 2/3 ( x + 9)?
(-5, 9)
(5, -9)
(2/3, 5)
(9, - 5)
(- 9, 5)
To find the point that is located on the line represented by the equation, substitute the x-coordinate and solve for the corresponding y-coordinate.
Let's check each option:
Option 1: (-5, 9)
Substituting x = -5 into the equation:
9 - 5 = (2/3)(-5 + 9)
4 = (2/3)(4)
4 = 8/3
The equation is not true for this point.
Option 2: (5, -9)
Substituting x = 5 into the equation:
-9 - 5 = (2/3)(5 + 9)
-14 = (2/3)(14)
-14 = 28/3
The equation is not true for this point.
Option 3: (2/3, 5)
Substituting x = 2/3 into the equation:
5 - 5 = (2/3)(2/3 + 9)
0 = (2/3)(19/3)
0 = 38/9
The equation is not true for this point.
Option 4: (9, -5)
Substituting x = 9 into the equation:
-5 - 5 = (2/3)(9 + 9)
-10 = (2/3)(18)
-10 = 12
The equation is not true for this point.
Option 5: (-9, 5)
Substituting x = -9 into the equation:
5 - 5 = (2/3)(-9 + 9)
0 = (2/3)(0)
0 = 0
The equation is true for this point.
Therefore, the answer is (-9, 5).