41) Une $$ r $$ has an equation of $$ y+10=-2(x-6) $$. Une $$ s $$ is perpendicular to line $$ r $$ and passes through $$ (1,2) $$. What is the equavon of line $$ s $$ ?

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To find the equation of line $$ s $$ that is perpendicular to line $$ r $$ and passes through the point $$ (1,2) $$, we need to follow these steps:

1. Find the slope of line $$ r $$ from the given equation.
2. Determine the slope of line $$ s $$ as the negative reciprocal of the slope of line $$ r $$.
3. Use the point-slope form of a linear equation to find the equation of line $$ s $$ that passes through the point $$ (1,2) $$.

Let's start by finding the slope of line $$ r $$ from the given equation $$ y+10=-2(x-6) $$.

1. Rearrange the equation to the slope-intercept form $$ y = mx + b $$, where $$ m $$ is the slope and $$ b $$ is the y-intercept.

$$ y+10=-2(x-6) $$
$$ y+10=-2x+12 $$
$$ y=-2x+2 $$

From the equation, we can see that the slope of line $$ r $$ is -2.

2. The slope of line $$ s $$ is the negative reciprocal of the slope of line $$ r $$. Therefore, the slope of line $$ s $$ is $$ \frac{1}{2} $$.

3. Now, we can use the point-slope form of a linear equation to find the equation of line $$ s $$ that passes through the point $$ (1,2) $$. The point-slope form is given by:
$$ y - y_1 = m(x - x_1) $$
where $$ (x_1, y_1) $$ is the given point and $$ m $$ is the slope.

Substitute the values into the point-slope form:
$$ y - 2 = \frac{1}{2}(x - 1) $$

Simplify the equation to find the equation of line $$ s $$.
Solve the equation $$ y - 2 = \frac{1}{2}(x - 1) $$.
Solve the equation by following steps:
- step0: Solve for $$y$$:
  $$y-2=\frac{1}{2}\left(x-1\right)$$
- step1: Multiply the terms:
  $$y-2=\frac{1}{2}x-\frac{1}{2}$$
- step2: Move the constant to the right side:
  $$y=\frac{1}{2}x-\frac{1}{2}+2$$
- step3: Calculate:
  $$y=\frac{x+3}{2}$$
The equation of line $$ s $$ is $$ y = \frac{x+3}{2} $$.
The equation of line $$ s $$ is $$ y = \frac{x+3}{2} $$.

Une has an equation of . Une is perpendicular to line and passes
through . What is the equavon of line ?

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Une has an equation of . Une is perpendicular to line and passes through . What is the equavon of line ?