Math ! 62 points for answer(s) right answers only, and credible reasoning .

question 1) which interval on the graph could be described as linear increasing?

a
b
c
d

question 2) which of the following best describes interval b on the graph shown?

linear constant

linear decreasing

linear increasing

nonlinear increasing

question 3) keisha ran to swim practice but needed to stop by her friend natasha’s house on the way. she stayed at natasha’s house for 15 minutes, and together they ran the rest of the way to practice, where they stayed for 1 hour.

which graph best represents the scenario described?

which graph best represents the scenario described?

a coordinate plane graph is shown. the axis is labeled time and the y-axis is labeled distance from home in blocks. a line begins at 0 comma 5, decreases to 0.25 comma 2, stays horizontal to 0.6 comma 2, then increases to 0.75 comma 9. the line is horizontal to 1.75 comma 9.

a coordinate plane graph is shown. the axis is labeled time and the y-axis is labeled distance from home in blocks. a line begins at 0 comma 0, increases to 0.3 comma 2, increases to 0.5 comma 5, then increases to 0.75 comma 9. the line decreases to 1.75 comma 0, where it touches the axis.

a coordinate plane graph is shown. the x-axis is labeled time and the y-axis is labeled distance from home in blocks. a line begins at 0 comma 0, increases to 0.25 comma 5, stays horizontal until 0.5 comma 5, then increases to 0.75 comma 9. the line is horizontal until 1.75 comma 9.

a coordinate plane graph is shown. the axis is labeled time and the y-axis is labeled distance from home in blocks. a line begins at 0 comma 5, is horizontal to 0.3 comma 5, increases to 0.5 comma 6, is horizontal to 0.8 comma 6, then increases to 1.75 comma 9

question 4) the graph shown represents the water level in kayla’s bathtub as a function of time:

which description would best explain what was happening during kayla’s bath during interval c on the graph?

kayla ran water to fill the bathtub.

kayla emptied the tub.

kayla got into the bathtub.

kayla soaked in the bathtub

Question #1, refers to the graph that appears on the left:

The graph is comprised of 4 segments.
All of the segments are linear.
Segment 'B' is the only one that's rising.

Question #2, also refers to the graph that appears on the left:

As discussed in the answer to Question #1,
interval-B is a segment that's linear and rising.

Question #3:

Keisha runs to Natasha's house, stays there for 15 minutes,
then ... with Natasha ... runs the rest of the way to swim practice.

If the story is graphed, the graph has 3 segments.  Since the slope
of each segment is Keisha's speed during that interval:
-- the middle segment will have no slope, while she sits motionless
at Natasha's house;
-- the 1st and 3rd segments will have positive slopes, while Keisha
is running.

Choice A).  Terrible choice.  It says that at time=0, when Keisha begins
running, she is 5 blocks from home.  Then it says that the line decreases,
as if she runs from there toward her house.  Not a good choice.

Choice B).  Somewhat better, but doesn't fit the story.  This graph
says that she starts from her house, runs at 3 different speeds
until she is 9 blocks away, then immediately turns around and
spends the next hour running back home.  Also not a good choice.

Choice C).  This is it.  If I had not read the story and just saw this graph,
I could see that Keisha started at her house, ran 5 blocks away from in
0.25 hour, stayed at that -place for the next 0.25 hour, then ran to some
place that was 9 blocks from her house in another 0.25 hour, and finally,
stayed there for the next hour.  That's all the information that appears on
this graph, but it certainly matches the story, and additionally tells us
how long she stayed at swim practice.

Choice D).  Now that we know we have a good graph in choice-C,
this one is not only wildly wrong, but it's funny too.
This graph says that at time zero, Keisha is 5 blocks away from her
house, and she stays right there for 0.3 hour.  She moves 1 block
from there in the next 0.2 hour, then stays at THAT place for the next
0.3 hour, and finally proceeds steadily to 9 blocks from her house
over the next 0.95 hour.

Question #4.    Refers to the graph on the right side.     

This graph is comprised of 5 linear segments.  The slope of
each segment is the rate at which the level of water in the tub
is changing.  A rising line says that the water level is rising.
A falling line says that the water level is falling.  If the water
level isn't changing, then the slope of the line is zero ... it's
a horizontal segment.

Before we even look at the story, let's look at the graph:

Segment A:  the tub is empty at time zero, then rises slowly
                       for about 8 minutes;
Segment B:  suddenly at 8 minutes, the level rises by 50%
                       (from level 20 to level 30) in 2 minutes or less;
Segment C:  for the next 15 minutes, the level doesn't change;
Segment D:  the water drops quickly to level-20 in 2 minutes or less;
Segment E:  in about 8 minutes, the water level drops slowly to zero.

If somebody told us that this was the graph of a girl taking a bath,
we could just about read the story from the graph:
A:  filling the tub from the faucets ... takes 8 minutes;
B:  the person slowly and carefully getting into the tub, making the level rise
C:  the person in the tub;
D:  the person slowly and carefully getting out of the tub;
E:  the tub emptying in 8 minutes.

Now I'm ready to look at the choices.

OK.  I see that the question is only asking about segment-C.

K ran water to fill the tub ... No.  The level isn't changing.
K emptied the tub ... No.  The level isn't changing.
K got into the tub ... No.  The level isn't changing.
K soaked in the bathtub ... Yes !  The level isn't changing.

Question #1

The graph is comprised of 4 segments. They are usually numbered I, II, III and IV. We also know that all of the segments are linear.

⇒Segment 'B' is the answer.

Question #2,

We know that interval-B is a segment that's linear and is rising (Going up).

Question #3:

Keisha ran to swim practice but needed to stop by her friend Natasha’s house on the way. She stayed at Natasha’s house for 15 minutes, and together they ran the rest of the way to practice, where they stayed for 1 hour. 

If we graph this there will be 3 segments because the slope 
of each segment is Keisha's speed during that interval:

⇒ the middle segment will have no slope,which makes the slope undefined.

⇒ the 1st and 3rd segments will have positive slopes, If a line has a positive slope, variable y always increases when x increases. 

Choice A).  Terrible choice.  

Choice B). Terrible choice.  

Choice C).  This is the correct answer. It includes all the information that appears on the given graph, and it matches the given story.

Choice D).  Terrible choice.  

Question #4.     

Kayla soaked in the bathtub is the correct choice. 

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