Write a function rule that relates X and Y.
1. (-2,0), (-1,1), (0,2), (1,3), (2,4)
2. (-3,-5), (0,1), (3,7), (6,13), (9,19)
To find the function rule that relates X and Y in each set of coordinates, we need to observe the pattern or relationship between the X and Y values.
1. For the first set of coordinates: (-2,0), (-1,1), (0,2), (1,3), (2,4)
Looking at the Y values, we can see that they increase by 1 each time as X increases by 1. This suggests a linear relationship where Y is equal to X plus a constant.
To find the constant, we can use any of the given coordinates. Let's take the first one: (-2,0).
If we substitute X = -2 into the equation Y = X + C, we get:
0 = -2 + C
C = 2
Therefore, the function rule that relates X and Y in this case is: Y = X + 2.
2. For the second set of coordinates: (-3,-5), (0,1), (3,7), (6,13), (9,19)
To find the pattern or relationship between X and Y in this case, let's examine the differences between consecutive Y values:
-5 - 1 = -6
1 - (-5) = 6
7 - 1 = 6
13 - 7 = 6
We can observe that the difference is constant and equal to 6 in every case. This implies a linear relationship where Y is equal to a constant times X plus another constant.
To find the constants, let's take the first coordinate: (-3, -5).
Substituting X = -3 and Y = -5 into the equation Y = AX + B, we get:
-5 = -3A + B
Now, let's take another coordinate, for example, (0, 1).
Substituting X = 0 and Y = 1 into the equation Y = AX + B, we get:
1 = 0A + B
B = 1
We can now substitute B = 1 back into the first equation to find A:
-5 = -3A + 1
-3A = -6
A = 2
Therefore, the function rule that relates X and Y in this case is: Y = 2X + 1.