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The problem provided is as follows:

"In the Cartesian coordinate system \( xy \), consider the point \( A(0, 3) \). Determine the equation of the line that passes through point \( A \) and has a slope equal to 1."

### Solution:

To find the equation of the line, we can use the point-slope form of a linear equation:

\[
y - y_1 = m(x - x_1)
\]

where:
- \( m \) is the slope of the line,
- \( (x_1, y_1) \) is a point on the line.

Given:
- Point \( A(0, 3) \) means \( x_1 = 0 \) and \( y_1 = 3 \),
- Slope \( m = 1 \).

Substituting these values into the point-slope form:

\[
y - 3 = 1(x - 0)
\]

Simplifying this equation:

\[
y - 3 = x
\]

Finally, we add 3 to both sides to get the equation of the line:

\[
y = x + 3
\]

So, the equation of the line is **\( y = x + 3 \)**.

Would you like more details or have any other questions?

### Related Questions:
1. What would the equation of the line be if the slope were \( -1 \) instead?
2. How do you find the slope of a line given two points on the line?
3. Can you determine the equation of a line parallel to \( y = x + 3 \) that passes through a different point?
4. What is the equation of the line perpendicular to \( y = x + 3 \) that passes through point \( A(0, 3) \)?
5. How does changing the slope affect the angle of the line with respect to the x-axis?

### Tip:
When working with linear equations, the slope tells you how steep the line is. A positive slope means the line goes upwards from left to right, while a negative slope means it goes downwards.

Learn how to find the equation of a line passing through point A(0, 3) with a slope of 1 using the point-slope form of a linear equation. This problem involves basic coordinate geometry concepts and is suitable for students in Grades 7-9.

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