Look at the following points.
(4, 0), (3, −1), (6, 3), (2, −4)
Which are solutions to y = x − 4? Choose all correct answers.
To check whether a point is a solution to the equation y = x − 4, we substitute the x and y values into the equation and see if the equation is satisfied.
For the points (4, 0):
0 = 4 - 4
0 = 0
Yes, this point is a solution to the equation.
For the points (3, -1):
-1 = 3 - 4
-1 = -1
Yes, this point is a solution to the equation.
For the points (6, 3):
3 = 6 - 4
3 = 2
No, this point is not a solution to the equation.
For the points (2, -4):
-4 = 2 - 4
-4 = -2
No, this point is not a solution to the equation.
Therefore, the correct answers are: (4, 0) and (3, -1).
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 check each point one by one:
Point (4, 0):
Substituting x = 4 and y = 0 into the equation, we get:
0 = 4 - 4
0 = 0
Since the equation holds true, the point (4, 0) is a solution to y = x - 4.
Point (3, -1):
Substituting x = 3 and y = -1 into the equation, we get:
-1 = 3 - 4
-1 = -1
Since the equation holds true, the point (3, -1) is a solution to y = x - 4.
Point (6, 3):
Substituting x = 6 and y = 3 into the equation, we get:
3 = 6 - 4
3 = 2
Since the equation does not hold true, the point (6, 3) is not a solution to y = x - 4.
Point (2, -4):
Substituting x = 2 and y = -4 into the equation, we get:
-4 = 2 - 4
-4 = -2
Since the equation does not hold true, the point (2, -4) is not a solution to y = x - 4.
Therefore, the correct solutions to the equation y = x - 4 are (4, 0) and (3, -1).
To determine which points are solutions to the equation y = x - 4, we need to substitute the x and y values from each point into the equation and check if the equation holds true.
Let's go through each point one by one:
1. (4, 0):
Substituting x = 4 and y = 0 into the equation, we get:
0 = 4 - 4
0 = 0
The equation holds true. So, (4, 0) is a solution.
2. (3, -1):
Substituting x = 3 and y = -1 into the equation, we get:
-1 = 3 - 4
-1 = -1
The equation holds true. So, (3, -1) is a solution.
3. (6, 3):
Substituting x = 6 and y = 3 into the equation, we get:
3 = 6 - 4
3 = 2
The equation does not hold true. So, (6, 3) is not a solution.
4. (2, -4):
Substituting x = 2 and y = -4 into the equation, we get:
-4 = 2 - 4
-4 = -2
The equation does not hold true. So, (2, -4) is not a solution.
Therefore, the solutions to the equation y = x - 4 are (4, 0) and (3, -1).