Question

which of the graphs has the greatest rate of change? a graph a b graph b c graph c d graph d

Explanation:

Step1: Define rate of change

Rate of change = $\frac{\Delta y}{\Delta x}$ (slope)

Step2: Calculate slope for Graph A

From graph: $\Delta x=8$, $\Delta y=2$. Slope = $\frac{2}{8}=0.25$

Step3: Calculate slope for Graph B

From graph: $\Delta x=3$, $\Delta y=8$. Slope = $\frac{8}{3}\approx2.67$

Step4: Calculate slope for Graph C

From graph: $\Delta x=8$, $\Delta y=4$. Slope = $\frac{4}{8}=0.5$

Step5: Calculate slope for Graph D

From graph: $\Delta x=6$, $\Delta y=8$. Slope = $\frac{8}{6}\approx1.33$

Step6: Compare all slopes

$2.67 > 1.33 > 0.5 > 0.25$

Answer:

B. Graph B