Question

estimate the slope of the graph at the points ((x_1, y_1)) and ((x_2, y_2)).
slope at ((x_1, y_1)) (\boxed{0})
slope at ((x_2, y_2)) (\boxed{})

Explanation:

Step1: Identify slope at $(x_1,y_1)$

The red tangent line at $(x_1,y_1)$ is horizontal, so its slope is $0$.

Step2: Calculate slope at $(x_2,y_2)$

The red tangent line at $(x_2,y_2)$ rises 1 unit for every 1 unit run. Use slope formula: $\text{slope}=\frac{\Delta y}{\Delta x}=\frac{1}{1}=1$.

Answer:

slope at $(x_1, y_1)$: $0$
slope at $(x_2, y_2)$: $1$