Question

you are collecting data about the melting rates of blackfoot glacier. the graph and table show the average thickness of the glacier, in meters, as a function of time in years since 2020.

1. find the rate of change for blackfoot glacier. show exactly how you calculated the change in y, and change in x, the overall rate of change. write your answer as a whole number or a fraction in simplest form.
2. describe what the rate of change means in this context.
3. find the y - intercept for blackfoot glacier.
4. describe what the y - intercept means in this context.
5. using the rate of change and y - intercept, create the equation for blackfoot glacier in slope - intercept form, y = mx + b.

Explanation:

Step1: Calculate change in y and x

Let's take two points (0, 150) and (15, 110). $\Delta y=110 - 150=-40$, $\Delta x=15 - 0 = 15$.

Step2: Find rate of change (slope)

Rate of change $m=\frac{\Delta y}{\Delta x}=\frac{-40}{15}=-\frac{8}{3}$.

Step3: Identify y - intercept

From the table, when $x = 0$, $y = 150$, so y - intercept $b = 150$.

Step4: Create equation

The equation in slope - intercept form is $y=-\frac{8}{3}x + 150$.

Answer:

1. Rate of change: $-\frac{8}{3}$
2. It means the glacier's thickness decreases by $\frac{8}{3}$ meters per year.
3. y - intercept: 150
4. It's the glacier's thickness in 2020.
5. $y=-\frac{8}{3}x + 150$