Question

functions - 8.f.2
examine the following sets of functions and determine which one has a greater rate of change.

1. a:

b: $y = 2x + 3$
greater rate of change: _______________

Explanation:

Step1: Find slope of A

Identify two points on line A, e.g., \((-3, 0)\) and \((0, 1)\) (or others). Use slope formula \(m = \frac{y_2 - y_1}{x_2 - x_1}\).
\(m_A = \frac{1 - 0}{0 - (-3)} = \frac{1}{3}\).

Step2: Find slope of B

The equation \(y = 2x + 3\) is in slope - intercept form \(y = mx + b\), so slope \(m_B = 2\).

Step3: Compare slopes

Compare \(m_A=\frac{1}{3}\) and \(m_B = 2\). Since \(2>\frac{1}{3}\), \(m_B>m_A\).

Answer:

B (or the function \(y = 2x+3\))