Question

jackie, an oceanographer, used satellite technology to measure the depth of gull bay over several years. the bays depth changed gradually during this time. this situation can be modeled as a linear relationship. chart: x-axis time (years) from 0 to 10, y-axis bays depth (centimeters) from 380 to 389, line with y-intercept 381 what does the slope of the line tell you about the situation?

Explanation:

Step1: Identify variables

The x - axis is time (years), and the y - axis is bay's depth (centimeters). The linear relationship is between time and depth.

Step2: Recall slope formula

The slope of a line is given by $m=\frac{\Delta y}{\Delta x}$, where $\Delta y$ is the change in the y - variable and $\Delta x$ is the change in the x - variable.

Step3: Analyze the slope's meaning

For this graph, $\Delta y$ is the change in the bay's depth (in centimeters) and $\Delta x$ is the change in time (in years). So the slope $m = \frac{\text{Change in Bay's Depth}}{\text{Change in Time}}$. From the graph, as time (x) increases, the depth (y) also increases. Let's take two points, for example, when $x = 0$, $y=381$ and when $x = 3$, $y = 382$. Then $\Delta y=382 - 381=1$ and $\Delta x=3 - 0 = 3$, so the slope is $\frac{1}{3}\approx0.33$ centimeters per year. This means that the slope represents the rate of change of the bay's depth with respect to time. Specifically, it tells us how much the bay's depth increases (since the slope is positive) per year.

Answer:

The slope of the line represents the rate at which the depth of Gull Bay changes per year. Since the slope is positive, it tells us that the depth of Gull Bay increases over time, and the value of the slope (e.g., if we calculate it, we can find the exact number of centimeters) is the amount by which the bay's depth increases each year. For example, from the graph, we can see that as time increases by a certain number of years, the depth increases proportionally, and the slope gives the rate of this increase (e.g., approximately $\frac{1}{3}$ centimeters per year or other calculated value based on more precise points) .