Question

what is the function rule for the linear function in this table? slope-intercept form y=mx+b input (x) 0 1 2 3 output (y) 6 5 4 3

Explanation:

Step1: Find the slope (m)

The slope \( m \) is calculated as \( \frac{y_2 - y_1}{x_2 - x_1} \). Using the points \( (0, 6) \) and \( (1, 5) \), we get \( m=\frac{5 - 6}{1 - 0}=\frac{-1}{1}=-1 \).

Step2: Find the y - intercept (b)

When \( x = 0 \), \( y = 6 \). In the slope - intercept form \( y=mx + b \), when \( x = 0 \), \( y=b \). So \( b = 6 \).

Step3: Write the function rule

Substitute \( m=-1 \) and \( b = 6 \) into \( y=mx + b \). We get \( y=-x + 6 \).

Answer:

The function rule is \( y=-x + 6 \)