Introduction:
When a number is divided by another number, the result obtained is called the quotient and the remaining part is called the remainder. In this given problem, we are given that the quotient is 9 and the remainder is 1. We need to express this information in the form of a linear equation.

Understanding the problem:
To solve the problem, we need to determine the original number and the number by which it is divided. We are given the quotient as 9 and the remainder as 1. Let's assume the original number as 'x' and the number it is divided by as 'y'.

Expressing the information in a linear equation:
To express the given information in the form of a linear equation, we can use the equation:
x = y * quotient + remainder

In this case, the equation becomes:
x = y * 9 + 1

Explanation:
The equation x = y * 9 + 1 represents the relationship between the original number (x), the number it is divided by (y), the quotient (9), and the remainder (1).

This equation states that the original number (x) can be obtained by multiplying the number it is divided by (y) with the quotient (9), and then adding the remainder (1).

Solution:
To find the exact values of 'x' and 'y', we need additional information. Given only the quotient and remainder, there are multiple possible values for 'x' and 'y' that satisfy the equation x = y * 9 + 1.

For example:
- x = 91, y = 10 (as 91 divided by 10 gives a quotient of 9 and a remainder of 1)
- x = 181, y = 20 (as 181 divided by 20 gives a quotient of 9 and a remainder of 1)

Hence, the equation x = y * 9 + 1 represents the relationship between the original number, the number it is divided by, the quotient, and the remainder. However, to find the specific values of 'x' and 'y', we need more information.