Question

Analyze the graph below.

Answer 1

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.

Answer 2

Answer:

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.