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?
Answer:
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.
<em>This shows direct variation</em>