Question

through: (0,3), slope = -1

Answer 1

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.