3. Look at the following points.
(4, 0), (3, −1), (6, 3), (2, −4)
Which are solutions to y = x − 4? Choose all correct answers.
(2 points)
(6, 3)
(4, 0)
(3, −1)
(2, −4)
So it would be (4,0) and (3,-1)?
you got it
Just sub in the given point to see if the equation is true.
e.g. for (6,3)
is 3 = 6-3 ?? , NO, so (6,3) is not a solution
etc.
or
To me the equation simply says that the y value is 4 less than the x value, so by just looking at the given points, I can tell .
e.g. (4, 0) , is 0 four less than 4 ? , YUP!
etc
sup
Well, let me tell you a little joke before we get into the answers. Why don't scientists trust atoms?
Because they make up everything!
Now, let's solve these points and find the solutions to y = x - 4.
For the first point (4, 0), let's substitute x with 4:
0 = 4 - 4
0 = 0
Since the equation is true, (4, 0) is a solution.
For the second point (3, -1), let's substitute x with 3:
-1 = 3 - 4
-1 = -1
This means that (3, -1) is also a solution.
For the third point (6, 3), let's substitute x with 6:
3 = 6 - 4
3 = 2
Oops! Looks like this point doesn't satisfy the equation, so (6, 3) is not a solution.
Finally, for the fourth point (2, -4), let's substitute x with 2:
-4 = 2 - 4
-4 = -2
Again, this point doesn't satisfy the equation, so (2, -4) is not a solution either.
Therefore, the correct solutions to y = x - 4 are:
- (4, 0)
- (3, -1)
I hope that puts a smile on your face!
To determine which points are solutions to the equation y = x - 4, you need to substitute the x and y values of each point into the equation and check if it satisfies the equation.
Let's go through each point one by one:
1. Point (6, 3):
Substituting the x and y values into the equation:
3 = 6 - 4
3 = 2
This equation is NOT true. Therefore, (6, 3) is NOT a solution to y = x - 4.
2. Point (4, 0):
Substituting the x and y values into the equation:
0 = 4 - 4
0 = 0
This equation is true. Therefore, (4, 0) is a solution to y = x - 4.
3. Point (3, -1):
Substituting the x and y values into the equation:
-1 = 3 - 4
-1 = -1
This equation is true. Therefore, (3, -1) is a solution to y = x - 4.
4. Point (2, -4):
Substituting the x and y values into the equation:
-4 = 2 - 4
-4 = -2
This equation is NOT true. Therefore, (2, -4) is NOT a solution to y = x - 4.
From the analysis, the correct answers are:
- (4, 0)
- (3, -1)
So the correct options are:
(4, 0)
(3, -1)