Look at the following points. (1,4), (8,5), (0, 3), (2, -1)
Show your work. Which are solution to y = x- 3? Choose all that are correct.
a) (1, 4)
b) (8, 5)
c) (0, 3)
d) (2, -1)
To check which points are solutions to the equation y = x - 3, we substitute the x-coordinate of each point into the equation and see if it equals the y-coordinate.
a) (1, 4):
4 = 1 - 3
4 = -2 (Not a solution, since the equation is not true)
b) (8, 5):
5 = 8 - 3
5 = 5 (Solution, since the equation is true)
c) (0, 3):
3 = 0 - 3
3 = -3 (Not a solution, since the equation is not true)
d) (2, -1):
-1 = 2 - 3
-1 = -1 (Solution, since the equation is true)
The correct solutions to y = x - 3 are b) (8, 5) and d) (2, -1).
To determine which points are solutions to the equation y = x - 3, we substitute the x-values of each point into the equation and check if the resulting y-value matches the given y-coordinate of the point.
Let's go through each point:
a) (1, 4):
Substituting x = 1 into the equation, we have:
4 = 1 - 3
4 = -2
Since this equation is not true, (1, 4) is not a solution to y = x - 3.
b) (8, 5):
Substituting x = 8 into the equation, we have:
5 = 8 - 3
5 = 5
Since this equation is true, (8, 5) is a solution to y = x - 3.
c) (0, 3):
Substituting x = 0 into the equation, we have:
3 = 0 - 3
3 = -3
Since this equation is not true, (0, 3) is not a solution to y = x - 3.
d) (2, -1):
Substituting x = 2 into the equation, we have:
-1 = 2 - 3
-1 = -1
Since this equation is true, (2, -1) is a solution to y = x - 3.
Therefore, the correct solutions to y = x - 3 are:
b) (8, 5)
d) (2, -1)