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emmasim [6.3K]
2 years ago
8

Select the correct answer.

Mathematics
1 answer:
vagabundo [1.1K]2 years ago
3 0

Answer:

b: -23 -25

Step-by-step explanation:

im sorry if its not correct

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A family on vacation records the time in hours) and the distance (in miles) that they travel. The data are shown in the scatter
nata0808 [166]

Answer:

In the first 3.5 hours, the family travelled 175 miles.

Step-by-step explanation:

We have the table:

time (hours)              distance ( miles)

      0                                   0

      1                                   50

       2                                 100

      3                                  150

      4                                 200

      5                                 250

      6                                 300

      7                                 350

      8                                 400

      9                                 450

This seems like a linear relationship, let's write the general line:

y = a*x + b

That represents this situation, y is the distance in miles and x is the time in hours.

In the line equation, a represents the slope and b the y-intercept.

And if the line passes through the points (x₁, y₁) and (x₂, y₂), then the slope of the line is:

a = (y₂ - y₁)/(x₂ - x₁)

In this case we have a lot of points for the line, we can use any pair we want (we actually should use a few different pairs to see that the slope is always the same)

So if we use the first two (0, 0) and (1, 50)

the slope is:

a = (50 - 0)/(1 - 0) = 50

Now, if we use the third and fifth points (4, 200) and (5, 250) now the slope is:

a = (250 - 200)/(5 - 4) = 50/1 = 50

So we can conclude that the slope of the equation is a = 50

Then the equation is something like:

y = 50*x + b

To find the value of b, we can use any of the points of the line, for example (0, 0)

This means that when x = 0, y also must be 0, then:

0 = 50*0 + b

0 = b

Then the equation is:

y = 50*x

Now, to answer how many miles the family travelled in the first 3.5 hours, we just need to replace x by 3.5 in the equation:

y = 50*3.5 = 175

In the first 3.5 hours, the family travelled 175 miles.

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2 years ago
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Answer:

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Rewrite in slope-intercept form.

Tap for more steps...

y

=

3

2

x

Use the slope-intercept form to find the slope and y-intercept.

Tap for more steps...

Slope:  

3

2

y-intercept:  

(

0

,

0

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Any line can be graphed using two points. Select two  

x

values, and plug them into the equation to find the corresponding  

y

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Tap for more steps...

x

y

0

0

2

3

Graph the line using the slope and the y-intercept, or the points.

Slope:  

3

2

y-intercept:  

(

0

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x

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0

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image of graph

Step-by-step explanation:

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