Answer: A. initial value 12, rate of change -2
Step-by-step explanation:
Find the rate of change and the initial value for the linear relation.
[tex]\left[\begin{array}{ccc}x&y\\1&10\\2&8\\3&6\\4&4\end{array}\right][/tex]
Step 1: Use the two of the points from the table above and solve for the slope = rate of change.
(1, 10) (2, 8)
[tex]\frac{y_{2} - y_{1} }{x_{2} - x_{1} }[/tex] = [tex]\frac{8-10}{2-1}[/tex] = [tex]\frac{-2}{1}[/tex] = -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)
[tex]\left[\begin{array}{ccc}y=10\\m=-2\\x=1\\b = ?\end{array}\right][/tex]
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.
