Question

What is the rate of change and initial value for the linear relation that includes the points shown in the table?

X. 1 2 3 4
Y. 10 8 6 4

A) initial value 12, rate of change -2
B) initial value 8, rate of change 2
C) initial value 12, rate of change 2
D) initial value 8, rate of change -2

Answer 1

Answer: A. initial value 12, rate of change -2

Explanation:

Find the rate of change and the initial value for the linear relation.

`\left[\begin{array}{ccc}x&y\\1&10\\2&8\\3&6\\4&4\end{array}\right]`

Step 1: Use the two of the points from the table above and solve for the slope = rate of change.

(1, 10) (2, 8)

`(y_(2) - y_(1) )/(x_(2) - x_(1) )` =
`(8-10)/(2-1)` =
`(-2)/(1)` = -2

Step 2: Using the slope plug it into the slope-intercept form to solve for the initial value or b.

y = mx + b (1, 10)

`\left[\begin{array}{ccc}y=10\\m=-2\\x=1\\b = ?\end{array}\right]`

10 = -2(1) + b

10 = -2 + b

+2 +2

12 = b

The initial value of the linear reaction would be 12 and the rate of change is -2.