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)
make a table
dx is change in x
dy is change in y
d2 means the change in dx and dy
x y dx dy d2x d2y
-2 0
-1 1
****** 1 1
0 2
****** 1 1
1 3
****** 1 1
2 4
Oh, no need to go any further, the change in x over the change in y (the slope m) is constant, 1/1 = 1
therefore we have a straight line
y = m x + b
put any old given point in to find b (0,2) for example
2 = 1 (0) + b
b = 2
so
y = x + 2
Do the second one the same way. You will find dy/dx = m = 4/3
reversed dy and dx
Oh, no need to go any further, the change in y over the change in x (the slope m) is constant, 1/1 = 1
Hint: both are straight lines.
#1 has a slope of 1 and a y-intercept of 2.
#2 has a slope of 2 and a y-intercept of 1.
Now if I had put those third and fourth columns in, I would have gotten the change in dy and the change in dx.
In this case it was zero so I knew it was a straight line (constant slope):
make a table
dx is change in x
dy is change in y
d2 means the change in dx and dy
x y dx dy d2x d2y
-2 0
****** 1 1
-1 1 ************ 0 0
****** 1 1
0 2 ************ 0 0
****** 1 1
1 3 ************ 0 0
****** 1 1
2 4
To find the function rule that relates X and Y, we need to look for a pattern in the given sets of coordinates.
For the first set of coordinates:
1. (-2,0)
2. (-1,1)
3. (0,2)
4. (1,3)
5. (2,4)
By observing the pattern, we can see that for every X value, the Y value increases by 1. Thus, the function rule is Y = X + 1.
For the second set of coordinates:
1. (-3,-5)
2. (0,1)
3. (3,7)
4. (6,13)
5. (9,19)
In this case, the pattern is not as obvious. However, if we subtract the X value from the Y value, we get the following results:
1. (-3 - (-5)) = 2
2. (0 - 1) = -1
3. (3 - 7) = -4
4. (6 - 13) = -7
5. (9 - 19) = -10
By observing this pattern, we can see that subtracting X from Y always gives a constant value of -2. Therefore, the function rule is Y = X - 2.