4) The quantities x and y are in proportion x 4 30 8 __b__ a) b) c) y 6 45 __a__ 15 Find the value of a and b. Find the constant of variation. Is it direct variation or inverse variation?

Question:

The quantities x and y are in proportion

x      y

4      6

30   45

8      b

a      15

(a) Find the values of a and b.

(b) Find the constant of variation. Is it direct variation or inverse variation?

and

Constant of variation is 1.5

Direct Variation

Step-by-step explanation:

Solving (a): The values of a and b

First, we determine the equation that relates x and y

From the table, we have:

The slope (m) is:

The equation is then calculated using:

This gives:

Solving for the value of b

From the table: x = 8, y = b

Substitute these values in

Solving for the value of a

From the table: x = a, y = 15

Substitute these values in

Solve for a

Solving (b): The constant of variation.

This has been solved in (a) above as:

Direct or Inverse?

From the given table, we notice that y increases as x increases and y decreases as x decreases.

This shows direct variation