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.
