Determine which three out of the six points shown below are a solution to the equation x, plus, y, equals, 1, .x+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.
left bracket, minus, 8, comma, 9, right bracket(−8,9), left bracket, 0, comma, 1, right bracket(0,1), left bracket, minus, 4, comma, 1, right bracket(−4,1), left bracket, minus, 1, comma, 0, right bracket(−1,0), left bracket, 0, comma, 5, right bracket(0,5), left bracket, minus, 2, comma, 3, right bracket(−2,3)
To determine which points are solutions to the equation x + y = 1, we can simply substitute the x and y values of each point into the equation and see if it equals 1.
1) (-8,9):
-8 + 9 = 1
1 = 1
2) (0,1):
0 + 1 = 1
1 = 1
3) (-4,1):
-4 + 1 = 1
-3 = 1 (not equal)
4) (-1,0):
-1 + 0 = 1
-1 = 1 (not equal)
5) (0,5):
0 + 5 = 1
5 = 1 (not equal)
6) (-2,3):
-2 + 3 = 1
1 = 1
The points (-8,9), (0,1), and (-2,3) are the solutions to the equation x + y = 1.
Now, let's plot these three points on a graph and draw a line through them.
-8 | .
9 | .
| .
| .
| .
| .(0,1)
| .
| .
| .(-2,3)
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-10 -5 0 5 10
The line passing through the points (-8,9), (0,1), and (-2,3) will look like a diagonal line that slops downward from left to right.