# The equation in which y is directly proportional to x .

### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

#### Solutions

Chapter 1, Problem 33RCC

(a)

To determine

## To write: The equation in which y is directly proportional to x.

Expert Solution

The equation in which the y is directly proportional to x is y=kx .

### Explanation of Solution

Directly proportional is the condition in which there is always a constant ratio between them. This constant is called as the proportionality constant.

As one variable change, another variable changes at the same rate.

In the direct relation one quantity is constant multiple of the other.

If quantity directly related to x and y,

yx=ky=kx

Here,

• k is some constant.

Thus, the equation in which the y is directly proportional to x is y=kx .

(b)

To determine

### To write: The equation in which y is inversely proportional to x.

Expert Solution

The equation in which the y is inversely proportional to x is y=kx .

### Explanation of Solution

Inversely proportional is the condition in which the product of two variables is constant.

As one variable decreases, another variable increases at the same rate.

If a quantity inversely proportional to another quantity,

xy=ky=kx

Here,

• k is some constant.

Thus, the equation in which the y is inversely proportional to x is y=kx .

(c)

To determine

### To write: The equation in which z is jointly proportional to x and y.

Expert Solution

The equation in which z is jointly proportional to x and y is z=kxy .

### Explanation of Solution

Jointly proportional is the condition in which one variable is dependent jointly with the other variable.

As one variable is directly proportional to each variable taken one at a time.

If a quantity is jointly proportional to another quantity,

z=kxy

Here,

• k is some constant.

Thus, the equation in which z is jointly proportional to x and y is z=kxy .

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