Question

which of these linear functions has a greater slope? function a graph of a line with points plotted function b $y = \frac{5}{6}x + 7$ options: function a, function b

Explanation:

Step1: Find slope of Function A

Using two points \((x_1,y_1)=(1,3)\) and \((x_2,y_2)=(2,4)\) (from the graph), slope \(m_A=\frac{y_2 - y_1}{x_2 - x_1}=\frac{4 - 3}{2 - 1}=1=\frac{6}{6}\).

Step2: Compare slopes

Slope of Function B is \(m_B = \frac{5}{6}\). Since \(\frac{6}{6}>\frac{5}{6}\), \(m_A>m_B\).

Answer:

Function A