Find the slope of a line perpendicular to the line whose equation is 3, x, plus, y, equals, 83*x*+*y*=8. Fully simplify your answer.

We are given the equation of a line \( 3x + y = 8 \), and we need to find the slope of a line perpendicular to this line.

### Step 1: Find the slope of the given line
The equation of the line is in standard form: 
\[
3x + y = 8
\]

To find the slope, we need to rewrite this equation in slope-intercept form \( y = mx + b \), where \( m \) is the slope.

Let's solve for \( y \):
\[
y = -3x + 8
\]

From this equation, the slope \( m_1 \) of the given line is \( -3 \).

### Step 2: Find the slope of the perpendicular line
The slope of a line perpendicular to another is the negative reciprocal of the original slope. Since the slope of the given line is \( -3 \), the slope \( m_2 \) of the perpendicular line will be:
\[
m_2 = \frac{1}{3}
\]

### Final Answer:
The slope of the line perpendicular to \( 3x + y = 8 \) is \( \frac{1}{3} \).

Would you like further clarification on any step or more details?

Here are 5 related questions for further practice:
1. What is the slope of a line perpendicular to \( 4x - y = 2 \)?
2. How do you find the slope of a line parallel to \( 2x + 5y = 10 \)?
3. What is the equation of a line with slope \( \frac{1}{3} \) and passing through the point \( (2, 5) \)?
4. How do you convert a line from standard form to slope-intercept form?
5. What is the general formula for the slope of a perpendicular line?

**Tip:** The negative reciprocal of a slope \( m \) is always \( -\frac{1}{m} \).

Find the slope of a line perpendicular to the line whose equation is 3x + y = 8. Fully simplify your answer.

Learn how to find the slope of a line perpendicular to the line 3x + y = 8 with a step-by-step guide. This problem involves rewriting the equation into slope-intercept form and applying the perpendicular slopes theorem. Ideal for students in Grades 8-10.

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