Acaterpillar 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?

The value of y is

Step-by-step explanation:

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 line passes through the origin

therefore

Is a proportional variation

Find the value of k

with the point

The equation is equal to

so

For

substitute

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

we know that

applying the law of sines

°

so

∠j=18°

∠k=29°

∠l=180-(18+29)=133°

the answer part a) is

the measure of angle k is  ≈29°

part b)  the measure of angle k could also be

(180-29)=151°

so

∠j=18°

∠k=151°

∠l=180-(18+151)=11°

the answer part b) is

the measure of angle k could also be 151°

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