Find the slope of a line perpendicular to the line whose equation is x, minus, y, equals, 3x−y=3. Fully simplify your answer.
To find the slope of a line perpendicular to the given line, we need to find the slope of the given line first.
The given line is in the form of: x - y = 3x - y = 3.
Rearranging the equation, we get:
x - y = 3x - y - 3.
Combining like terms, we have:
0 = 2x - 3.
Isolating x, we get:
2x = 3.
x = 3/2.
Thus, the slope of the given line is undefined (denoted by a vertical line) since there is no y-component in the equation.
For a line perpendicular to the given line, the slope is the negative reciprocal of the slope of the given line.
Since the slope of the given line is undefined, the slope of the line perpendicular to it is 0 (denoted by a horizontal line).