Look at the following points.
(4, 0), (3, −1), (6, 3), (2, −4)
Which are solutions to y = x − 4? Choose all correct answers.
(1 point)
Responses
(6, 3)
(6, 3)
(4, 0)
(4, 0)
(3, −1)
(3, −1)
(2, −4)
(2, −4)
All of the given points are solutions to y = x - 4. Therefore, all of the options are correct:
(6, 3)
(4, 0)
(3, -1)
(2, -4)
To determine which points are solutions to the equation y = x - 4, we need to substitute the x and y values of each point into the equation and check if the equation holds true.
Let's go through each point one by one:
1. Point (4, 0):
Substituting the x and y values into the equation:
0 = 4 - 4
0 = 0
The equation holds true. Therefore, (4, 0) is a solution to y = x - 4.
2. Point (3, -1):
Substituting the x and y values into the equation:
-1 = 3 - 4
-1 = -1
The equation holds true. Therefore, (3, -1) is a solution to y = x - 4.
3. Point (6, 3):
Substituting the x and y values into the equation:
3 = 6 - 4
3 = 2
The equation does not hold true. Therefore, (6, 3) is not a solution to y = x - 4.
4. Point (2, -4):
Substituting the x and y values into the equation:
-4 = 2 - 4
-4 = -2
The equation does not hold true. Therefore, (2, -4) is not a solution to y = x - 4.
Thus, the correct solutions are:
- (4, 0)
- (3, -1)