Question

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)

Answer 1

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

Answer 2

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

Answer 3

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.

Answer 4

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