Answer:1/3
Step-by-step explanation:
To find the slope of the line perpendicular to 3x + y = 1, we first need to determine the slope of the given line and then find the negative reciprocal to obtain the slope of the perpendicular line.
1. **Convert the Equation to Slope-Intercept Form:**
Rewrite the given equation 3x + y = 1 in the form y = mx + b, where m is the slope:
y = -3x + 1
2. **Identify the Slope:**
From the equation in slope-intercept form, we see that the slope of the given line is -3.
3. **Find the Slope of the Line Perpendicular:**
The slope of a line perpendicular to another line is the negative reciprocal of the original line's slope. In this case, the slope of the perpendicular line will be the negative reciprocal of -3, which is 1/3.
Therefore, the slope of the line perpendicular to 3x + y = 1 is 1/3.
