Respuesta :
How to Solve The Constant of Proportionality of a Non Proportional Graph?
We apply our knowledge on the direct and inverse variations, identify them and then determine the constant of proportionality and thereby get the solutions to our problems.
Example 1:
Find the constant of proportionality, if y=24 and x=3 and y ∝ x.
Solution: We know that y varies proportionally with x. We can write the equation of the proportional relationship as y = kx. Substitute the given x and y values, and solve for k.
24 = k (3)
k = 24 ÷ 3 = 8
Therefore, the constant of proportionality is 8.
Example 2:
4 workers take 3 hours to finish the desired work. If 2 more workers are hired, in how much time will they complete the work?
Solution:
Let x1 = number of workers in case 1 = 4
x2 = Number of workers in case 2 = 6
y1 = number of hours in case 1 = 3
y2 = number of hours in case 2 = To be found
If the number of workers is increased, the time taken to complete will reduce. We find that number of workers is inversely proportional to the time taken, (y1 = k/x1) ⇒ 3 = k / 4⇒ k = 12
Again, to find the number of hours, (y2 = k/x2) ⇒ y2 = 12/6 = 2 hours.
