Question

the line models the depth of the water in a small fountain during a severe rainstorm. what is the y - intercept? the y - intercept is \square. depth of the water in a fountain depth of water (inches) number of hours

Explanation:

Step1: Understand y-intercept definition

The y - intercept of a line is the value of \( y \) (depth of water here) when \( x = 0 \) (number of hours \( = 0 \)).

Step2: Locate \( x = 0 \) on the graph

Looking at the graph, when the number of hours (\( x \)) is 0, we check the corresponding depth of water (\( y \)) value. From the graph, at \( x = 0 \), the depth of water is 6 inches? Wait, no, wait. Wait, the x - axis is "Number of Hours" and y - axis? Wait, no, looking at the graph labels: the vertical axis (y - axis) is "Depth of Water (inches)"? Wait, no, the horizontal axis (x - axis) is "Number of Hours" (from 0 to 15), and the vertical axis (y - axis) is "Depth of Water (inches)"? Wait, no, the blue line: when x (number of hours) is 0, what is y (depth)? Wait, the graph shows that when x = 0 (number of hours = 0), the depth (y) is 6? Wait, no, wait the first point on the line: when x = 0 (number of hours), the depth is 6? Wait, no, looking at the grid: the x - axis (number of hours) starts at 0, and the y - axis (depth) starts at 0. Wait, the blue line passes through (0, 6)? Wait, no, the first marked point is at (0, 6)? Wait, the graph: the x - axis is "Number of Hours" (0, 3, 6, 9, 12, 15), and the y - axis is "Depth of Water (inches)" (0, 3, 6, 9, 12, 15). The blue line starts at (0, 6)? Wait, no, the first point is at (0, 6)? Wait, when x = 0 (number of hours = 0), the depth of water is 6 inches? Wait, no, maybe I got the axes reversed. Wait, the label "Depth of Water (inches)" is on the horizontal axis? No, the horizontal axis is labeled "Number of Hours" (from 0 to 15) on the left, and "Depth of Water (inches)" (0, 3, 6, 9, 12, 15) on the top. Wait, no, the graph is a bit confusing, but the key is: the y - intercept is the value of y when x = 0. In a linear model, the y - intercept is the point where the line crosses the y - axis (x = 0). Looking at the graph, when x (number of hours) is 0, the depth of water (y) is 6? Wait, no, wait the blue line: when x = 0 (number of hours = 0), the depth is 6. Wait, but let's check the line equation. Alternatively, the y - intercept is the value of y when x = 0. From the graph, the line intersects the y - axis (x = 0) at y = 6? Wait, no, maybe I made a mistake. Wait, the first point on the line is at (0, 6), so the y - intercept is 6. Wait, but let's confirm: the y - intercept is the value of the dependent variable (depth) when the independent variable (number of hours) is 0. So when x = 0 (no hours have passed), the depth is 6 inches. So the y - intercept is 6.

Answer:

6