Determine which three out of the six points shown below are a solution to the equation x, plus, y, equals, 8, .x+y=8. Plot the three points that are in the solution set, draw a line through the three points and then answer the questions below.
(6,2) (0,8) (4,4) (3,3) (7,3) (6,6)
To determine which points are solutions to the equation x+y=8, we need to substitute the x and y values of each point into the equation and see if the equation holds true.
Substituting the x and y values of each point:
(6,2): 6+2=8 (Yes, this point is a solution)
(0,8): 0+8=8 (Yes, this point is a solution)
(4,4): 4+4=8 (Yes, this point is a solution)
(3,3): 3+3=6 (No, this point is not a solution)
(7,3): 7+3=10 (No, this point is not a solution)
(6,6): 6+6=12 (No, this point is not a solution)
So, the three points that are solutions to the equation x+y=8 are: (6,2), (0,8), and (4,4).
Now let's plot these three points on a graph:
- The point (6,2) is 6 units to the right on the x-axis and 2 units up on the y-axis.
- The point (0,8) is at the origin, 0 units on the x-axis and 8 units up on the y-axis.
- The point (4,4) is 4 units to the right on the x-axis and 4 units up on the y-axis.
Now we can draw a line passing through these three points.
The line through the points (6,2), (0,8), and (4,4) looks like this:
|
|
| * *
| * *
| * *
|*_______________*
(0,8)
Now let's answer the questions below:
1. Is (3,3) a solution to x+y=8? No.
2. Is (7,3) a solution to x+y=8? No.
3. Is (6,6) a solution to x+y=8? No.