What is the slope of the line that is perpendicular to the line y + 4 = -5/3(x - 6)?

We are tasked with finding the slope of the line perpendicular to the line given by the equation:

\[
y + 4 = -\frac{5}{3}(x - 6)
\]

### Step 1: Identify the slope of the given line.
The equation is in **point-slope form**: 
\[
y - y_1 = m(x - x_1)
\]
where \(m\) is the slope.

In this case, the slope \(m\) of the given line is \( -\frac{5}{3} \).

### Step 2: Find the slope of the perpendicular line.
The slope of a line perpendicular to another line is the **negative reciprocal** of the original slope. 

The negative reciprocal of \( -\frac{5}{3} \) is:
\[
\frac{3}{5}
\]

### Conclusion:
The slope of the line perpendicular to \( y + 4 = -\frac{5}{3}(x - 6) \) is \( \frac{3}{5} \).

Would you like more details or have any questions?

Here are 5 related questions for further practice:
1. What is the slope of a line perpendicular to a line with a slope of \( \frac{2}{7} \)?
2. How would you convert the point-slope form to slope-intercept form?
3. If a line has a slope of 4, what is the slope of a line parallel to it?
4. Find the equation of the line perpendicular to \( y - 2 = 3(x + 1) \) and passing through (1, 2).
5. How do you determine if two lines are perpendicular by their slopes?

**Tip:** Always remember that the product of the slopes of two perpendicular lines is \(-1\).

Discover how to calculate the slope of a line perpendicular to y + 4 = -5/3(x - 6) using the concept of negative reciprocals. This problem involves key algebraic principles like point-slope form and the relationship between slopes of perpendicular lines. Suitable for students in Grades 9-11.

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