Question

function a and function b are linear functions.
function a
x | -6 | 1 | 9
---|---|---|---
y | -7 | 7 | 23
function b
$y = 3x$
which statement is true?
the slope of function a is greater than the slope of function b.
the slope of function a is less than the slope of function b.

Explanation:

Step1: Find slope of Function A

Use slope formula \( m = \frac{y_2 - y_1}{x_2 - x_1} \). Take points \((-6, -7)\) and \((1, 7)\).
\( m_A = \frac{7 - (-7)}{1 - (-6)} = \frac{14}{7} = 2 \).

Step2: Find slope of Function B

Function B is \( y = 3x \), so slope \( m_B = 3 \) (from \( y = mx + b \), \( m = 3 \)).

Step3: Compare slopes

\( m_A = 2 \), \( m_B = 3 \). So \( 2 < 3 \), meaning slope of A is less than B.

Answer:

The slope of Function A is less than the slope of Function B.