Determine which three out of the six points shown below are a solution to the equation 3, x, plus, y, equals, 5, .3x+y=5. Plot the three points that are in the solution set, draw a line through the three points and then answer the questions below.
left bracket, 4, comma, minus, 7, right bracket(4,−7), left bracket, minus, 3, comma, 4, right bracket(−3,4), left bracket, minus, 2, comma, minus, 9, right bracket(−2,−9), left bracket, 0, comma, 5, right bracket(0,5), left bracket, 1, comma, 2, right bracket(1,2), left bracket, 1, comma, minus, 8, right bracket(1,−8)
To determine which points are solutions to the equation 3x + y = 5, we can substitute the x and y values of each point into the equation and check if the equation holds true.
Let's substitute the x and y values of each point one by one:
1. For the point (4, -7):
3(4) + (-7) = 12 - 7 = 5
The equation is true for this point.
2. For the point (-3, 4):
3(-3) + 4 = -9 + 4 = -5
The equation is not true for this point.
3. For the point (-2, -9):
3(-2) + (-9) = -6 - 9 = -15
The equation is not true for this point.
4. For the point (0, 5):
3(0) + 5 = 0 + 5 = 5
The equation is true for this point.
5. For the point (1, 2):
3(1) + 2 = 3 + 2 = 5
The equation is true for this point.
6. For the point (1, -8):
3(1) + (-8) = 3 - 8 = -5
The equation is not true for this point.
Based on these calculations, the three points that are solutions to the equation are:
(4, -7), (0, 5), and (1, 2).
Now, let's plot these three points on a graph and draw a line passing through them:
```
|
| +
| +
| +
| +
|_____+__________
1 2 3 4 5
```
The line passing through (4, -7), (0, 5), and (1, 2) would look roughly like this:
```
|
| +
| +
|_______________
\
\
\
\
\
```
Answering the question:
- Which three points are in the solution set? (4, -7), (0, 5), and (1, 2).
- What does the line represent? The line represents all the points (x, y) that satisfy the equation 3x + y = 5.