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) 4 10 16 22

Explanation:

Step1: Find the slope \( m \)

The slope \( m \) of a linear function is calculated by the formula \( m=\frac{y_2 - y_1}{x_2 - x_1} \). Using the points \( (0, 4) \) and \( (1, 10) \), we have \( m=\frac{10 - 4}{1 - 0}=\frac{6}{1} = 6 \).

Step2: Find the y - intercept \( b \)

The y - intercept \( b \) is the value of \( y \) when \( x = 0 \). From the table, when \( x = 0 \), \( y = 4 \), so \( b = 4 \).

Step3: Write the function rule

Using the slope - intercept form \( y=mx + b \), with \( m = 6 \) and \( b = 4 \), the function rule is \( y=6x + 4 \).

Answer:

\( y = 6x+4 \)