Question

which of these linear functions has a smaller slope? function a input (x) 0 1 2 output (y) 4 7 10 function b y = (1/3)x + 7 function b function a

Explanation:

Step1: Find slope of Function A

The slope \( m \) of a linear function is calculated by \( m=\frac{y_2 - y_1}{x_2 - x_1} \). For Function A, using points \((0, 4)\) and \((1, 7)\):
\( m_A=\frac{7 - 4}{1 - 0}=\frac{3}{1} = 3 \).

Step2: Find slope of Function B

Function B is in slope - intercept form \( y = mx + b \), where \( m \) is the slope. For \( y=\frac{1}{3}x + 7 \), the slope \( m_B=\frac{1}{3} \).

Step3: Compare slopes

Compare \( m_A = 3 \) and \( m_B=\frac{1}{3} \). Since \( \frac{1}{3}<3 \), the slope of Function B is smaller.

Answer:

Function B