The students in Mrs. Willow's reading class are all reading the same novel independently. Four students create a graph of their reading rates, in words per minute, as shown below. Which student reads the fastest? A. Sarah B. Mason C. Charlie D. Riley

see the explanation

Step-by-step explanation:

Let

x ----> the time in minutes

y ---> the number of words reading

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form or

In a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin

In this problem, the relationship between x, and y, represent a proportional variation

The linear equation is equal to

where

k is the constant of proportionality or the reading rate in words per minute

therefore

The student who reads fastest is the one whose equation has the highest proportionality constant or whose graph has the steepest line slope

Example

If you have

The student who reads fastest is the number 3

Because the value of k=50 words/minute is greater

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let f (x ) is a function and c be a positive real number,   the graph of the function g (x ) = f (cx ) is represented as follows.

when, c > 1,   the function compresses it in the x - direction.

when, 0 < c < 1, the function stretches it.

the function is g ( x ) = (9x )2.

the heighest power of x in g ( x ) = (9x )2 is 2, so the parent function is square function.

the equation of parent function is f ( x ) = x 2 .

the function is g ( x ) = (9x )2 and the parent function is f ( x ) = x 2 .

so, the functions f and g have the following relationship.

g ( x ) = f ( 9x ).

compare the function g ( x ) = f ( 9x ) with g (x ) = f (cx ).

c = 9 ( > 1 ).

so, the function g (x ) = (9x )2 compresses it in the x - direction.

step-by-step explanation: