Direct Inverse and Joint Variation Word Problems

TL;DR

This video explains how to write and solve equations for direct, inverse, and joint variation word problems.

Transcript

in this video we're going to go over direct inverse and joint variation word problems so the first thing that you need to be able to do is you need to be able to write the equation so we're going to focus on that and then we'll apply that in solving word problems so let's begin if y varies directly with x the equation that you need is y is equal to... Read More

Key Insights

• ❣️ Direct variation equations are of the form y = kx, where y and x are directly proportional.
• 🕡 Inverse variation equations are of the form y = k/x, where y and x are inversely proportional.
• ❣️ Joint variation equations are of the form y = kxr, where y varies jointly with x and r.
• 😉 The constant of variation, k, can be found by using the given values in the equation.
• 🔑 Solving word problems involving variations requires writing the correct equation and using the given values to find the unknown variable.
• 📁 Direct and inverse variations have different effects on the relationship between y and the changing variable.
• 📁 It is important to understand the concept of direct, inverse, and joint variation to correctly solve word problems.

Questions & Answers

Q: What is the equation for direct variation?

The equation for direct variation is y = kx, where y and x are directly proportional. As x increases, y increases proportionally, and vice versa.

Q: How do you write an equation for inverse variation?

The equation for inverse variation is y = k/x. Inverse variation means that as x increases, y decreases proportionally, and vice versa.

Q: What is the equation for joint variation?

The equation for joint variation is y = kxr, where y varies jointly with x and r. This means that as both x and r increase, y increases proportionally.

Q: How would you solve a word problem involving direct variation?

To solve a direct variation problem, first, write the equation y = kx. Then, use the given values to find the constant of variation, k. Finally, plug in the known values to find the value of y when a certain x is given.

Q: What is the difference between direct and inverse variation?

In direct variation, as x increases, y increases proportionally. In inverse variation, as x increases, y decreases proportionally. The equations for direct and inverse variation reflect this relationship.

Q: Can you provide an example of a word problem involving joint variation?

Sure. Let's say y varies jointly with x and z, and y is 36 when x is 2 and z is 3. The equation would be y = kxz. To find the value of y when x is 4 and z is 6, plug in these values into the equation and solve for y.

Q: What does it mean when y varies directly with the square of x?

When y varies directly with the square of x, the equation is y = kx^2. This means that as x increases, y increases, but the relationship is quadratic, so the increase in y is not linear.

Q: How do you solve a word problem involving inverse variation?

To solve an inverse variation problem, write the equation y = k/x. Use the given values to find the constant of variation, k. Then, plug in the known values to find the value of y when a certain x is given.

Summary & Key Takeaways

• The video explains the equations for direct and inverse variation: y = kx and y = k/x, respectively.

• It also demonstrates how to write equations for joint variation, where y varies jointly with two variables: y = kxr.

• Several word problems are provided, along with step-by-step solutions to find the value of y for different values of x and z.