Which function has a greater unit rate?

Question

X: -3, -5, -9, -12
Y: 5, 3, -1, -4
A) Positive Slope
B) Negative Slope
C) No Slope
D) Undefined Slope

Answer 1

A) Positive Slope

To find the unit rate for each function, we can calculate the change in y over the change in x between consecutive points.

For function X:
-3 to -5: (3-5)/(-3 - -5) = 2/2 = 1
-5 to -9: (-1- -3)/(-5 - -9) = 2/4 = 0.5
-9 to -12: (-4- -1)/(-9 - -12) = 3/3 = 1

The unit rates are 1, 0.5, and 1 for function X.

For function Y:
5 to 3: (3-5)/(5-3) = -2/2 = -1
3 to -1: (-1-3)/(3- -1) = -4/4 = -1
-1 to -4: (-4- -1)/(-1 - -4) = -3/3 = -1

The unit rates are -1, -1, and -1 for function Y.

Since the unit rates for function X are all positive (1, 0.5, 1), it has a greater unit rate compared to function Y, where all the unit rates are -1.