Question

Use the table to answer the question.

Grade Words per minute
K 10
1 35
2 60
3 85
Lucia loves books. The table models Lucia’s reading speed from kindergarten to third grade. Write a function to model Lucia’s reading speed.

(1 point)
Responses

y=35x+10
y equals 35 x plus 10

y=25x
y equals 25 x

y=25x+10
y equals 25 x plus 10

y=10x+25

Answer 1

To model Lucia's reading speed based on the data provided in the table, we can look for a linear function in the form \( y = mx + b \), where \( y \) is the words per minute, \( x \) is the grade level, \( m \) is the slope (the rate of change in reading speed per grade), and \( b \) is the y-intercept (the reading speed in kindergarten).

From the table:
- In kindergarten (K, which we can treat as grade 0), \( y = 10 \) words per minute.
- In first grade (1), \( y = 35 \) words per minute.
- In second grade (2), \( y = 60 \) words per minute.
- In third grade (3), \( y = 85 \) words per minute.

Let's determine the slope \( m \):

1. The increase in reading speed from grade 0 (K) to grade 1 is \( 35 - 10 = 25 \).
2. The increase from grade 1 to grade 2 is \( 60 - 35 = 25 \).
3. The increase from grade 2 to grade 3 is \( 85 - 60 = 25 \).

So, the reading speed increases by 25 words per minute for each grade.

Using \( y = mx + b \):
- The slope \( m = 25 \).
- The y-intercept \( b = 10 \) (the reading speed at kindergarten).

Thus, the function that models Lucia's reading speed is:

\[ y = 25x + 10 \]

Therefore, the correct response is:

**y = 25x + 10** (y equals 25 x plus 10)