Question

use the graph of the function to complete the table.
input output
0 10
4 6
8

Explanation:

Step1: Analyze the graph's pattern

The graph is a straight line. From input \( x = 0 \), output \( y = 10 \); at \( x = 4 \), \( y = 6 \). The change in \( x \) is \( 4 - 0 = 4 \), change in \( y \) is \( 6 - 10 = - 4 \), so slope \( m=\frac{-4}{4}=-1 \). The equation is \( y=-x + 10 \) (since \( y \)-intercept is 10).

Step2: Find output for \( x = 8 \)

Substitute \( x = 8 \) into \( y=-x + 10 \). So \( y=-8 + 10 = 2 \). Alternatively, from \( x = 4 \) (output 6) to \( x = 8 \), \( x \) increases by 4, so \( y \) decreases by 4 (since slope is -1), \( 6-4 = 2 \).

Answer:

2