Answer:
Part 2
The rate of change is 1 in increase in forearm length per 1 inch increase in foot length
Part 3
1) Foot length = 17.922 in.
2) The rate of change of the equation y = 0.860·x + 3.302 in part A is 0.860
3) No the data does not correspond with part A
4) The data presented here has a greater rate of change
5) Different data sources
6) Yes
7) Yes
Step-by-step explanation:
Part 2
The data are as follows
Forearm Foot
9.25 8.5
10.25 9.5
9.75 9
10.75 10
8.75 8
To find the rate of change, we have;
For points
(x₁, y₁) = (9.25, 8.5) and (x₂, y₂) = (8.75, 8) we have;
Rate of change = (y₂ - y₁)/(x₂ - x₁) substituting the values we arrive at
(8.75 - 9.25)/(8 - 8.5) = 1
The rate of increase of foot to forearm is 1 to 1. That is there is an increase of 1 in in forearm length for every inch increase in foot length
The rate of change is 1 in increase in forearm length per 1 inch increse in foot length
Part 3
1) For a person with length of forearm, x = 17 inches long, we have;
Length of foot, y = 0.860·x + 3.302
Plugging in the values, we have;
y = 0.860×17 + 3.302 = 17.922 in.
2) The rate of change of the equation y = 0.860·x + 3.302 in part A is 0.860
3) No the data does not correspond with part A
4) The rate of change from part A = 0.860, Therefore, the data presented here has a greater rate of change
5) The values are different because of they are derived from a non corresponding sources
6) Yes the relation is a function because the length of the foot is a function of the length of the forearm
From the equation of a straight line, we have;
y = mx + c
Where:
m = Slope = 1
Therefore; for forearm, y = 9.25, we have
9.25 = 1×8.5 + c
∴ c = 9.5 - 8.5 = 1
The equation of the function becomes;
y = x + 1
7) for the equation in part A given by
y = 0.860·x + 3.302
Yes the equation in part A can represent a function because it maps each value of x to a unique value of y
