Analyze the graph below.
part a
does the graph show a direct variation?
a.
yes
b.
no
how do you know?
part b
can you determine the constant of proportionality?
a.
yes, i will put it in my explanation below.
b.
no, i will explain why i can't below.
explain why you can or cannot determine the constant of proportionality.
whoever answers this correctly will get 70 points and brainliest.

A) Look at the coordinates of the four dots:

(0,0) (150,50) (300,100) (450,150)

Divide the x's by the y's ( other than the (0,0) one:

150/50 = 3

300 / 100 = 3

450/150 = 3

The ratio is the same for all of them and the first set is (0,0) so it is a direct variation graph.

B) The constant of proportionality is the ratio found above by dividing the X values by the Y values, which is 3.

a) Yes, the graph shows a direct variation

b)Yes, the constant of proportionality can be determined

Step-by-step explanation:

Yes, the graph above shows a direct variation because as the value of y is increasing, the value of x is also increasing by the same factor which is 3.

Yes, the constant of proportionality can be determined.

According to direct variation, y is directly proportional to x i.e y = kx where k is the constant of proportionality.

Making k the subject of the formula, we will have;

k = y/x

The first coordinate on the graph shows that when y = 50, x = 150

k = 50/150

k = 1/3

Similarly for the second coordinate on the graph shows when y = 100, x = 300

k = 100/300

k = 1/3 at this coordinate.

And for the third coordinate on the graph shows when y = 150, x = 450

k = 150/450

k = 1/3 at this coordinate

Since the constant of proportionality are the same for each coordinate which is 1/3 this shows that as an increase in value of y gives rise to same increasing value of x and vice versa.

need more information

step-by-step explanation:

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for