Question

which of these linear functions has a greater slope? function a (a graph with points (0,2), (1,5), (2,8)) function b y = (3/2)x + 5 options: function b, function a

Explanation:

Step1: Find slope of Function A

Use two points \((0, 2)\) and \((1, 5)\) (from the graph). Slope formula: \(m=\frac{y_2 - y_1}{x_2 - x_1}\).
\(m_A=\frac{5 - 2}{1 - 0}=\frac{3}{1}=3\).

Step2: Find slope of Function B

Function B is \(y = \frac{3}{2}x + 5\), slope \(m_B=\frac{3}{2}=1.5\).

Step3: Compare slopes

\(3>1.5\), so \(m_A>m_B\).

Answer:

Function A