Question

jasmine is hiking at a state park. her distance from home, y, is a function of the time she hikes, x. rate of change: 2 initial value: 8 is an initial value of 8 reasonable? yes no

Explanation:

Step1: Recall the concept of initial value

The initial value is the value of $y$ when $x = 0$. In a linear - relationship $y=mx + b$, $b$ is the initial value. We can also use the slope - intercept form to check. First, find the slope $m=\frac{\Delta y}{\Delta x}$. Using the points $(2,12)$ and $(5,18)$, $m=\frac{18 - 12}{5 - 2}=\frac{6}{3}=2$. Then, using the point - slope form $y - y_1=m(x - x_1)$ with the point $(2,12)$ and $m = 2$, we have $y-12=2(x - 2)$. Expanding gives $y-12=2x-4$, or $y = 2x+8$. When $x = 0$, $y=8$.

Step2: Analyze from the graph

Looking at the graph, the line intersects the $y$ - axis at $y = 8$. This means when $x = 0$ (the start of hiking, time $x = 0$ hours), the distance from home $y$ is 8 miles.

Answer:

Yes