27. What is the gradient of the line that perpendicular to the line $$ (2 ext { Points })^{*} $$ $$ y=\frac{1}{3} x+5 $$ $$ \frac{1}{3} $$ 3 -3 $$ -\frac{1}{3} $$

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27. What is the gradient of the line that perpendicular to the line $$ (2 	ext { Points })^{*} $$ $$ y=\frac{1}{3} x+5 $$ $$ \frac{1}{3} $$ 3 -3 $$ -\frac{1}{3} $$

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To find the gradient of a line perpendicular to the given line $$ y = \frac{1}{3}x + 5 $$, follow these steps:

1. **Identify the Gradient of the Given Line:**
   - The equation $$ y = \frac{1}{3}x + 5 $$ is in the slope-intercept form $$ y = mx + c $$, where $$ m $$ is the gradient.
   - Therefore, the gradient ($$ m $$) of the given line is $$ \frac{1}{3} $$.

2. **Determine the Gradient of the Perpendicular Line:**
   - The gradient of a line perpendicular to another is the **negative reciprocal** of the original gradient.
   - Negative reciprocal of $$ \frac{1}{3} $$ is $$ -3 $$ (since $$ \frac{1}{3} $$ inverted is $$ 3 $$, and taking the negative gives $$ -3 $$).

**Answer:**  
$$-3$$
The gradient of the perpendicular line is -3.

What is the gradient of the line that
perpendicular to the line

3
-3

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