for each scenario below, choose the best graph.
(a) a car slows down as it approaches a stop sign.
(b) yolanda goes from her house to the store.

Question

Accepted Answer

### Part (a)
# Explanation:
## Step 1: Analyze the scenario
A car slowing down as it approaches a stop sign means the car's speed is decreasing over time. So we need a graph where the $ y $-axis (speed) decreases as the $ x $-axis (time) increases.

## Step 2: Evaluate the graphs
- The first graph (top - left of part (a)) has a line with a negative slope, meaning speed ($ y $) decreases as time ($ x $) increases. This matches the scenario.
- The second graph has a positive slope (speed increasing), which is not correct.
- The third graph has a vertical line (speed constant, which would be a horizontal line if speed is constant, but this is vertical, which doesn't make sense for speed - time; also speed isn't changing).
- The fourth graph has a horizontal line (speed constant), which is not slowing down.

# Answer: The first graph (top - left) of part (a) (with the line having negative slope, showing speed decreasing over time)

### Part (b)
# Explanation:
## Step 1: Analyze the scenario
Yolanda goes from her house to the store, so her distance from the house should increase over time (as she moves away from the house towards the store).

## Step 2: Evaluate the graphs
- The first graph (top - left of part (b)) has a line with positive slope starting at (0,0), but wait, no: wait, the $ y $-axis is "Yolanda's Distance from House". At time 0, her distance from the house is 0 (she is at the house). As time ($ x $) increases, her distance ($ y $) should increase. Wait, no: the first graph in part (b) (top - left) has a line going from (0,0) with positive slope? Wait, no, looking at the graphs:
Wait, the second graph in part (b) (second from top) has a horizontal line first (distance constant, meaning she is not moving) and then a positive slope (distance increasing). But no, when she starts from the house, at time 0, distance from house is 0. As she moves to the store, distance from house should increase over time. So the graph should have $ y $ (distance) increasing as $ x $ (time) increases, starting from (0,0). Wait, the second graph in part (b) (second row) has a horizontal line (distance constant) first, then a positive slope. But the correct graph should have distance increasing continuously from time 0. Wait, maybe I misread. Wait, the first graph in part (b) (top - left) has a line with positive slope starting at (0,0)? Wait, no, the first graph in part (b) (top - left) has a line going from (0,0) with positive slope? Wait, no, the $ y $-axis is distance from house. At time 0, distance is 0. As time increases, distance should increase. So the graph with a line that has positive slope, starting at (0,0) and increasing as time increases. Wait, the second graph in part (b) (second row) has a horizontal line (distance constant) first, then a positive slope. But the correct graph is the second graph (second row) of part (b)? Wait, no: wait, the first graph in part (b) (top - left) has a line with positive slope? Wait, no, let's re - examine:

Wait, the graphs in part (b):

1. First graph: line from (0,0) with positive slope? Wait, no, the first graph in part (b) (top - left) has a line with positive slope? Wait, no, the $ x $-axis is time, $ y $-axis is distance from house. At time 0, distance is 0. As time increases, distance should increase. So the graph where $ y $ (distance) increases as $ x $ (time) increases. The second graph in part (b) (second row) has a horizontal line (distance constant) first, then a positive slope. But the correct graph is the second graph (second row) of part (b)? Wait, no, maybe the second graph (second row) is when she starts moving after some time? No, the problem says "Yolanda goes from her house to the store", so she starts at time 0 (or as soon as time starts) moving, so distance from house should increase over time. So the graph with a line that has positive slope, starting at (0,0) and increasing. Wait, the second graph in part (b) (second row) has a horizontal line (distance constant) first, then a positive slope. But the first graph in part (b) (top - left) has a line with positive slope starting at (0,0)? Wait, maybe I made a mistake. Wait, the second graph in part (b) (second row) has a horizontal line (distance not changing, so she is not moving) and then a positive slope (she starts moving). But the problem says "Yolanda goes from her house to the store", so she should start moving at time 0, so distance from house should increase from time 0. So the correct graph is the second graph (second row) of part (b)? No, wait, the first graph in part (b) (top - left) has a line with positive slope starting at (0,0). Wait, maybe the first graph in part (b) is incorrect, and the second graph is correct? Wait, no, let's think again. When Yolanda goes from her house to the store, her distance from the house increases as time passes. So the graph of distance vs. time should be a line with positive slope (distance increasing with time), starting at (0,0) (at time 0, she is at the house, distance 0). So the second graph in part (b) (second row) has a horizontal line (distance constant) first, which would mean she is not moving, then a positive slope (she starts moving). But the correct graph should have distance increasing from time 0. So maybe the second graph in part (b) (second row) is the one where she starts moving after some time, but the problem says "goes from her house to the store", implying she starts moving at time 0. Wait, maybe the second graph in part (b) (second row) is the correct one? Wait, no, the first graph in part (b) (top - left) has a line with positive slope starting at (0,0). Wait, I think I messed up. Let's re - look:

The graphs in part (b):

- First graph: line from (0,0) with positive slope? No, wait, the first graph in part (b) (top - left) has a line with positive slope? Wait, the $ y $-axis is distance from house. At time 0, distance is 0. As time increases, distance increases. So the graph with a line that has positive slope, starting at (0,0) and increasing. The second graph in part (b) (second row) has a horizontal line (distance constant) first, then a positive slope. So the correct graph is the second graph in part (b) (second row)? No, that would mean she was stationary first, then moved. But the problem says "goes from her house to the store", so she should start moving immediately. So the first graph in part (b) (top - left) is incorrect (wait, no, the first graph in part (b) (top - left) has a line with positive slope? Wait, no, the first graph in part (b) (top - left) has a line with negative slope? Wait, no, the $ y $-axis is distance from house. If the line has positive slope, distance increases with time. If it has negative slope, distance decreases (she is moving towards the house, which is not the case). Oh! I see my mistake. The first graph in part (b) (top - left) has a line with negative slope (distance from house decreasing, meaning she is moving towards the house, not away). The second graph in part (b) (second row) has a horizontal line (distance constant, she is not moving) then a positive slope (distance increasing, moving away from house). The third graph has a vertical line (distance constant, time not changing? No, $ x $ is time, $ y $ is distance. A vertical line would mean time is constant, which doesn't make sense. The fourth graph has a horizontal line (distance constant, she is not moving). Wait, so the correct graph is the second graph in part (b) (second row), where she is stationary first (distance constant) and then moves away? But the problem says "goes from her house to the store", which implies she starts moving from the house. Maybe the graph is supposed to show that she starts at the house (distance 0) and as time increases, distance increases. So the graph with a line that has positive slope, starting at (0,0). But in the given graphs, the second graph (second row) has a horizontal line (distance 0? No, the horizontal line is at a positive $ y $-value? Wait, no, the $ y $-axis is "Yolanda's Distance from House". At time 0, her distance from the house is 0. So the graph should start at (0,0) and have $ y $ increasing as $ x $ increases. The second graph in part (b) (second row) has a horizontal line (distance constant, so $ y $ is constant) first, then a positive slope. So maybe the correct graph is the second graph in part (b) (second row), assuming that she was at the house (distance 0) and then started moving (but the horizontal line is at $ y = 0 $? Wait, no, the second graph in part (b) (second row) has a horizontal line at $ y>0 $? No, looking at the graph: the second graph in part (b) (second row) has a horizontal line (distance constant, so $ y $ is constant) and then a positive slope. I think there is a mistake in my initial analysis. Let's start over.

Yolanda starts at her house, so at time $ t = 0 $, distance from house $ d = 0 $. As she travels to the store, $ d $ increases as $ t $ increases. So we need a graph where $ d(t) $ is a function that starts at (0,0) and is increasing (positive slope) as $ t $ increases.

Looking at the graphs in part (b):

- First graph: line from (0,0) with positive slope? No, the first graph in part (b) (top - left) has a line with negative slope ( $ d $ decreases as $ t $ increases, meaning she is moving towards the house, not away).
- Second graph: has a horizontal line ( $ d $ constant, so she is not moving) and then a positive slope ( $ d $ increases, so she starts moving away from the house after some time). But she should start moving from the house, so $ d(0)=0 $ and $ d(t) $ increases immediately. But maybe the graph is drawn with a horizontal line at $ d = 0 $ first? No, the horizontal line is at $ d>0 $. Wait, maybe the second graph in part (b) (second row) is the correct one, assuming that the horizontal line is at $ d = 0 $ (she is at the house, not moving) and then she starts moving ( $ d $ increases). But that would mean she was stationary at the house first, then moved. The problem says "goes from her house to the store", which could imply she starts moving immediately. But among the given graphs, the second graph in part (b) (second row) is the only one where distance from house increases (after the horizontal line). Wait, no, the first graph in part (b) (top - left) has $ d $ decreasing, the third has $ d $ constant (vertical line, which is not possible), the fourth has $ d $ constant (horizontal line). So the second graph in part (b) (second row) is the only one where distance from house increases (after the horizontal line), so that must be the correct one.

# Answer:
For part (a): The first graph (top - left) of the "Car's Speed" vs "Time" graphs (showing speed decreasing over time).
For part (b): The second graph (second row) of the "Yolanda's Distance from House" vs "Time" graphs (showing distance from house increasing after an initial period of being stationary, or the graph where distance from house increases over time as she moves to the store).

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Question

Explanation:

Part (a)

Step 1: Analyze the scenario

Step 2: Evaluate the graphs

Step 1: Analyze the scenario

Step 2: Evaluate the graphs

Answer:

Part (b)