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Ksju [112]
3 years ago
10

Kyoko is reading a book by her favorite author. She read the first 20 pages in One-half of an hour. Reading at the same pace, Ky

oko wants to determine if she’ll have enough time to finish the book before she has to go to bed. Reading Time On a coordinate plane, a graph titled Reading Time has number of hours on the x-axis, and number of pages on the y-axis. A straight line goes through (0, 0), (0.5, 20), and (2, 80). According to the graph, which statement must be true? It will take her 2 hours to read 60 pages. It will take her 3 hours to read 120 pages. It will take her 4 hours to read 180 pages. It will take her 5 hours to read 210 pages.
Mathematics
1 answer:
eduard3 years ago
6 0

Answer:

It will take her 3 hours to read 120 pages.

Step-by-step explanation:

The number of pages read(y) after x hour can be modeled by a linear function in the following format:

y = ax + b

In which a is the number of pages read per hour and b is the initial number of pages read.

A straight line goes through (0, 0)

This means that when x = 0, y = 0

So

y = ax + b

0 = a*0 + b

b = 0

(0.5, 20)

When x = 0.5, y = 20

So

y = ax

20 = 0.5a

a = \frac{20}{0.5}

a = 40

The function in:

y(x) = 40x

According to the graph, which statement must be true?

It will take her 2 hours to read 60 pages.

y(2) = 40*2 = 80

Less than 2 hours for 60 pages, so this is false.

It will take her 3 hours to read 120 pages.

y(3) = 40*3 = 120

This statement is true.

It will take her 4 hours to read 180 pages.

y(4) = 40*4 = 160

More than 4 hours to read 180 pages. So false.

It will take her 5 hours to read 210 pages.

y(5) = 40*5 = 200

More than 5 hours to read 210 pages. So false.

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