Question

what is the vertical intercept for this line? this is the distance samara hiked when she was at the start of the nature trail. the slope is 150. the vertical intercept is \boxed{}.

Explanation:

Step1: Recall vertical intercept definition

The vertical intercept (y-intercept) of a line is the value of \( d \) when \( t = 0 \) (since \( t \) is the independent variable on the x - axis and \( d \) is the dependent variable on the y - axis).

Step2: Analyze the graph at \( t = 0 \)

Looking at the graph, when the time since the start of the hike (\( t \)) is 0 minutes (the start of the nature trail), the distance traveled (\( d \)) is the value at the point where \( t = 0 \). From the graph, the point at \( t = 0 \) has a \( d \)-value of 0? Wait, no, looking at the graph, the first point (at \( t = 0 \)) is at \( d = 0 \)? Wait, no, let's check the coordinates. The point at \( t = 0 \) is (0, 0)? Wait, no, the y - axis is distance traveled (ft) and x - axis is time (min). Wait, the graph has the first point at (0, 0)? Wait, no, the dot at \( t = 0 \) is at \( d = 0 \)? Wait, maybe I misread. Wait, the vertical intercept is the value of \( d \) when \( t = 0 \). From the graph, when \( t = 0 \) (time = 0, start of the hike), the distance \( d \) is 0? Wait, no, looking at the graph, the first point (the one at \( t = 0 \)) is at (0, 0)? Wait, the y - axis starts at 0, 50, 100, etc. The point at \( t = 0 \) is at \( d = 0 \)? Wait, no, maybe the dot at \( t = 0 \) is at \( d = 0 \). Wait, but let's think again. The vertical intercept is the y - intercept, which is the value of the dependent variable (d) when the independent variable (t) is 0. So when \( t = 0 \), what is \( d \)? From the graph, the point at \( t = 0 \) is (0, 0)? Wait, the graph shows that at \( t = 0 \), the distance \( d \) is 0? Wait, no, maybe I made a mistake. Wait, the y - axis is distance traveled, and at \( t = 0 \) (start), the distance should be 0, because she hasn't started hiking yet? Wait, but let's check the slope. The slope is 150, which is \( \frac{\Delta d}{\Delta t} \). For example, from \( t = 0 \) to \( t = 1 \), \( d \) goes from 0 to 150 (since slope is 150, \( \Delta d=150\times\Delta t \), when \( \Delta t = 1 \), \( \Delta d = 150 \)). So at \( t = 0 \), \( d = 0 \). So the vertical intercept is 0.

Answer:

0