Question

use the table to answer the question.
determining
the rate of
change
and initial
value from
x and y
values
x | y
2 | 22
8 | 25
determine the rate of change and the initial value of the linear function given here as a table of values.
(1 point)
the rate of change is m = \\(\square\\), and the initial value is b = \\(\square\\).

Explanation:

Step1: Calculate rate of change (slope)

The formula for rate of change (slope \( m \)) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is \( m = \frac{y_2 - y_1}{x_2 - x_1} \). Using points \((2, 22)\) and \((8, 25)\):
\( m = \frac{25 - 22}{8 - 2} = \frac{3}{6} = \frac{1}{2} \).

Step2: Find initial value (y-intercept \( b \))

Use the slope-intercept form \( y = mx + b \). Substitute \( m = \frac{1}{2} \) and a point (e.g., \( x = 2, y = 22 \)):
\( 22 = \frac{1}{2}(2) + b \)
\( 22 = 1 + b \)
Subtract 1 from both sides: \( b = 21 \).

Answer:

The rate of change is \( m = \frac{1}{2} \), and the initial value is \( b = 21 \).