Question

which of these linear functions has a greater slope? function a (a graph of a linear function with points plotted) function b y = \\(\frac{3}{2}\\)x + 3

Explanation:

Step1: Find slope of Function A

From the graph, points on Function A: (0, 4) and (2, 5). Slope formula: $m = \frac{y_2 - y_1}{x_2 - x_1}$. So $m_A = \frac{5 - 4}{2 - 0} = \frac{1}{2}$.

Step2: Slope of Function B

Function B: $y = \frac{3}{2}x + 3$. Slope $m_B = \frac{3}{2}$.

Step3: Compare slopes

$\frac{1}{2} = 0.5$, $\frac{3}{2} = 1.5$. Since $1.5 > 0.5$, $m_B > m_A$.

Answer:

Function B has a greater slope.