Determine which three out of the six points shown below are a solution to the equation 2x + y = 1. Plot the three points that are in the solution set, draw a line through the three points, and then answer the questions below.

(2,-3), (0,-4), (-2,-5), (5,-9),(-4,9),(6,-1)

Just sub the coordinates of each point into the equation to see if it satisfies

the equation.
I will do (-4,9)
LS = 2x + y
= 2(-4) + 9
= 1
RS = 1, Ahhh, the point (-4,9) is one of the points that lie on the line

Repeat for the others.
The graphing should be simple

Alright, let's take a look at these points and see which three are solutions to the equation 2x + y = 1.

(2,-3): We substitute x = 2 and y = -3 into the equation:
2(2) + (-3) = 4 - 3 = 1. Hey, this one works!

(0,-4): Let's plug in x = 0 and y = -4:
2(0) + (-4) = 0 - 4 = -4. Nope, this one doesn't fit the bill.

(-2,-5): Time to put x = -2 and y = -5 into the equation:
2(-2) + (-5) = -4 - 5 = -9. Nope, this one's out.

(5,-9): Replacing x = 5 and y = -9:
2(5) + (-9) = 10 - 9 = 1. We've got a winner!

(-4,9): Let's see if this one checks out with x = -4 and y = 9:
2(-4) + 9 = -8 + 9 = 1. It's a keeper!

(6,-1): Final test with x = 6 and y = -1:
2(6) + (-1) = 12 - 1 = 11. Nope, this one doesn't make the cut.

So, the three points that are solutions to the equation 2x + y = 1 are (2,-3), (5,-9), and (-4,9). Let's plot them on a graph and draw a line through them.

To determine which three points are a solution to the equation 2x + y = 1, we can substitute the x and y values of each point into the equation and check if it satisfies the equation.

Let's substitute the values of each point into the equation:

1. For the point (2,-3):
2(2) + (-3) = 4 - 3 = 1
This point satisfies the equation.

2. For the point (0,-4):
2(0) + (-4) = 0 - 4 = -4
This point does not satisfy the equation.

3. For the point (-2,-5):
2(-2) + (-5) = -4 - 5 = -9
This point does not satisfy the equation.

4. For the point (5,-9):
2(5) + (-9) = 10 - 9 = 1
This point satisfies the equation.

5. For the point (-4,9):
2(-4) + 9 = -8 + 9 = 1
This point satisfies the equation.

6. For the point (6,-1):
2(6) + (-1) = 12 - 1 = 11
This point does not satisfy the equation.

Therefore, the three points that are a solution to the equation are (2,-3), (5,-9), and (-4,9).

Now, let's plot these three points on a graph:

- The point (2,-3) corresponds to the coordinate (2,-3) on the graph.
- The point (5,-9) corresponds to the coordinate (5,-9) on the graph.
- The point (-4,9) corresponds to the coordinate (-4,9) on the graph.

After plotting these three points, draw a line through them.

Now, please let me know if you have any further questions.

To determine which three points out of the given six points are solutions to the equation 2x + y = 1, we can substitute the x and y values of each point into the equation and check if the equation holds true for each point.

Let's go through this process for each point:

1. (2,-3):
Substitute x = 2 and y = -3 into the equation:
2(2) + (-3) = 1
4 - 3 = 1
1 = 1

The equation holds true for the point (2,-3).

2. (0,-4):
Substitute x = 0 and y = -4 into the equation:
2(0) + (-4) = 1
0 - 4 = 1
-4 ≠ 1

The equation does not hold true for the point (0,-4).

3. (-2,-5):
Substitute x = -2 and y = -5 into the equation:
2(-2) + (-5) = 1
-4 - 5 = 1
-9 ≠ 1

The equation does not hold true for the point (-2,-5).

4. (5,-9):
Substitute x = 5 and y = -9 into the equation:
2(5) + (-9) = 1
10 - 9 = 1
1 = 1

The equation holds true for the point (5,-9).

5. (-4,9):
Substitute x = -4 and y = 9 into the equation:
2(-4) + 9 = 1
-8 + 9 = 1
1 = 1

The equation holds true for the point (-4,9).

6. (6,-1):
Substitute x = 6 and y = -1 into the equation:
2(6) + (-1) = 1
12 - 1 = 1
11 ≠ 1

The equation does not hold true for the point (6,-1).

Based on these calculations, the three points that are solutions to the equation 2x + y = 1 are (2,-3), (5,-9), and (-4,9).

To plot these three points, you can create a coordinate grid and mark each point on it. Then, draw a line passing through these three points.

I hope this helps!