Question

A caterpillar started at point (−2.5, −5.5) on a coordinate plane. She crawled in a straight line through the origin to point (45, y). What is y?

Answer 1

Answer: the value of y is 99

Starting point of the caterpillar = (−2.5, −5.5)

Crawled to the coordinate = (45, y)

y =?

Given that, it crawled in a straight line:

x and y are two variables that are directly proportional to one another

y/x = k

Where k is the constant of proportionality since it passes through the origin

-5.5/-2.5 = k

2.2 = k

So,

y/x = 2.2

So take the coordinate (45,y)

y =2.2 * 45

y = 99

Answer 2

The value of y is
`99`

Explanation:

we know that

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

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 line passes through the origin

therefore

Is a proportional variation

Find the value of k

with the point
`(-2.5,-5.5)`

`k=y/x=-5.5/-2.5=2.2`

The equation is equal to

`y=2.2x`

so

For
`x=45`

substitute

`y=2.2(45)=99`