Question 16 What is the slope of the line perpendicular to the line that passes through the points $$ (5,-2) $$ and $$ (3,6) $$ ? Submit Question

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To find the slope of the line perpendicular to the line that passes through the points $$ (5,-2) $$ and $$ (3,6) $$, we will follow these steps:

1. **Calculate the slope of the line through the given points.**
   The formula for the slope $$ m $$ between two points $$ (x_1, y_1) $$ and $$ (x_2, y_2) $$ is given by:
   $$
   m = \frac{y_2 - y_1}{x_2 - x_1}
   $$

2. **Determine the slope of the perpendicular line.**
   The slope of a line that is perpendicular to another line is the negative reciprocal of the original line's slope.

Let's start by calculating the slope of the line through the points $$ (5,-2) $$ and $$ (3,6) $$.

Let $$ (x_1, y_1) = (5, -2) $$ and $$ (x_2, y_2) = (3, 6) $$.

Now, we can calculate the slope $$ m $$.

$$
m = \frac{6 - (-2)}{3 - 5} = \frac{6 + 2}{3 - 5} = \frac{8}{-2} = -4
$$

Now that we have the slope of the original line, we can find the slope of the line that is perpendicular to it. The slope of the perpendicular line $$ m_{\perp} $$ is given by:

$$
m_{\perp} = -\frac{1}{m}
$$

Substituting the value of $$ m $$:

$$
m_{\perp} = -\frac{1}{-4} = \frac{1}{4}
$$

Thus, the slope of the line perpendicular to the line that passes through the points $$ (5,-2) $$ and $$ (3,6) $$ is $$ \frac{1}{4} $$.
The slope of the perpendicular line is $$ \frac{1}{4} $$.

Question 16 What is the slope of the line perpendicular to the line that passes through the points \( (5,-2) \) and \( (3,6) \) ? Submit Question

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