To find the equation of a line given a point it passes through and its slope, you can use the point-slope form of a linear equation:
\[ y - y_1 = m(x - x_1) \]
where \((x_1, y_1)\) is a point on the line and \(m\) is the slope.
Given:
- The point \((0, 3)\) (where \(x_1 = 0\) and \(y_1 = 3\))
- The slope \(m = -1\)
Substituting these values into the point-slope form gives:
\[ y - 3 = -1(x - 0) \]
This simplifies to:
\[ y - 3 = -x \]
Adding 3 to both sides yields:
\[ y = -x + 3 \]
So, the equation of the line is:
\[ y = -x + 3 \]
Alternatively, you can also express it in standard form \(Ax + By = C\):
\[ x + y = 3 \]
Both forms represent the same line.