Question Drought has affected the area for weeks. On the last day there was rain, the river had a depth of 12 feet. After 16 days rain, the depth is now 10 feet. What is the \( y \)-intercept in this situation? Do not include units in your answer.

To find the \( y \)-intercept in this situation, we can model the depth of the river over time. Let's denote: - \( x \) as the number of days since the last rain. - \( y \) as the depth of the river in feet. From the information given: 1. On the last day it rained (let's say this is day 0), the depth of the river was 12 feet. This gives us the point \( (0, 12) \). 2. After 16 days without rain, the depth of the river is now 10 feet. This gives us the point \( (16, 10) \). We can find the slope \( m \) of the line connecting these two points using the formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Substituting the points \( (0, 12) \) and \( (16, 10) \): \[ m = \frac{10 - 12}{16 - 0} = \frac{-2}{16} = -\frac{1}{8} \] Now we can use the point-slope form of the equation of a line, which is: \[ y - y_1 = m(x - x_1) \] Using the point \( (0, 12) \): \[ y - 12 = -\frac{1}{8}(x - 0) \] This simplifies to: \[ y - 12 = -\frac{1}{8}x \] Adding 12 to both sides gives us the equation of the line: \[ y = -\frac{1}{8}x + 12 \] In this equation, the \( y \)-intercept is the value of \( y \) when \( x = 0 \). From the equation, we see that the \( y \)-intercept is 12. Thus, the \( y \)-intercept in this situation is: \[ \boxed{12} \]