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) 1 5 9 13 y = ?x +

Explanation:

Step1: Find the y-intercept (b)

When \( x = 0 \), \( y = 1 \). In the slope - intercept form \( y=mx + b \), when \( x = 0 \), \( y=b \). So \( b = 1 \).

Step2: Calculate the slope (m)

We can use two points, for example, \( (x_1,y_1)=(0,1) \) and \( (x_2,y_2)=(1,5) \). The formula for slope \( m=\frac{y_2 - y_1}{x_2 - x_1} \).
Substitute the values: \( m=\frac{5 - 1}{1 - 0}=\frac{4}{1}=4 \).

Step3: Write the function rule

Using the slope - intercept form \( y = mx + b \), with \( m = 4 \) and \( b = 1 \), the function rule is \( y=4x + 1 \).

Answer:

\( y = 4x+1 \)