JOINTLY PROPORTIONAL

Jointly Proportional

Definition Of Jointly Proportional

If a variable z is jointly proportional to a set of variable x and y, the z = kxy, where k is the constant of proportionality.

More About Jointly Proportional

Jointly proportional is also known as joint variation.

Example of Jointly Proportional

The kinetic energy, E, of a moving object is jointly proportional to its mass, m, and the square of its speed, v.i.e., E = k .m. v²

Video Examples: Art of Problem Solving: Joint Proportion

Solved Example on Jointly Proportional

Ques: If x is jointly Proportional to y and z when x = 4, y = 8 and z = 9, then find the value of x when y = 2 and z = 18.

A. 1
B. 0
C. 2
D. 4
Correct Answer: C

Solution:

Step 1: x a k. y. z [joint proportional]
Step 2: x = k. y. z
Step 3: 4 = k. 8. 9 [Substituting the values for x, y, z.]
Step 4: k = 1/18[Simplify.]
Step 5: Therefore, x =1/18. 2. 18 [Substituting the values for k, y and z in x = k. y. z]
Step 6: So, x = 2 [Simplify.]

Quick Summary

Joint proportionality describes a relationship where one variable varies directly as the product of two or more other variables.
The equation z = kxy expresses the joint proportionality between z, x, and y, where k is a constant.
Joint proportionality is also known as joint variation.

\[ z = kxy \]

🍎 Teacher Insights

Use real-world examples, such as the area of a rectangle (A = lw) or the volume of a rectangular prism (V = lwh), to illustrate joint proportionality. Emphasize the importance of understanding the relationships between the variables.

🎓 Prerequisites

Ratio
Proportion
Direct Variation
Algebraic manipulation

Check Your Knowledge

Q1: If z is jointly proportional to x and y, and z = 24 when x = 2 and y = 3, find the value of z when x = 4 and y = 2.

16 32 48 64

Q2: Which equation represents that 'a' is jointly proportional to 'b' and the square of 'c'?

a = kb/c^2 a = kbc a = kbc^2 a = k(b + c^2)

Frequently Asked Questions

Q: What does jointly proportional mean?
A: Jointly proportional means that a variable varies directly as the product of two or more other variables. If z is jointly proportional to x and y, then z = kxy, where k is the constant of proportionality.

Q: How do I find the constant of proportionality?
A: To find the constant of proportionality, substitute known values of the variables into the equation and solve for k.