4) The equation of line $$ v $$ is $$ y-10=-y(x+2) $$. Une $$ w $$ indudes the point $$ (10,1) $$ and is perpendicular to line $$ v $$. What is the equation of line $$ w $$ ?

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To find the equation of line $$ w $$, we first need to determine the slope of line $$ v $$ from its given equation:

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

We can rearrange this equation to find the slope. First, let's distribute the right side:

$$
y - 10 = -yx - 2y
$$

Now, we can rearrange it to isolate $$ y $$:

$$
y + yx + 2y = 10
$$

This simplifies to:

$$
y(1 + x + 2) = 10
$$

$$
y(3 + x) = 10
$$

Now, we can express $$ y $$ in terms of $$ x $$:

$$
y = \frac{10}{3 + x}
$$

To find the slope of line $$ v $$, we can rewrite this in slope-intercept form $$ y = mx + b $$. However, it is easier to find the slope directly from the original equation. The equation can be rearranged to:

$$
y = -yx - 2y + 10
$$

This is a bit complex, so let's find the slope directly from the implicit form. The slope of line $$ v $$ can be found by differentiating or analyzing the equation.

From the equation $$ y - 10 = -y(x + 2) $$, we can see that the slope of line $$ v $$ is given by the coefficient of $$ x $$ when rearranged.

To find the slope of line $$ v $$, we can also rewrite it in a more standard form. Let's isolate $$ y $$:

$$
y + y(x + 2) = 10
$$

Factoring out $$ y $$:

$$
y(1 + x + 2) = 10
$$

This gives us:

$$
y(3 + x) = 10
$$

Thus, the slope $$ m_v $$ of line $$ v $$ is:

$$
m_v = -1
$$

Since line $$ w $$ is perpendicular to line $$ v $$, the slope $$ m_w $$ of line $$ w $$ will be the negative reciprocal of $$ m_v $$:

$$
m_w = -\frac{1}{m_v} = -\frac{1}{-1} = 1
$$

Now we have the slope of line $$ w $$ as $$ 1 $$. We also know that line $$ w $$ passes through the point $$ (10, 1) $$. We can use the point-slope form of the equation of a line:

$$
y - y_1 = m(x - x_1)
$$

Substituting $$ m = 1 $$, $$ x_1 = 10 $$, and $$ y_1 = 1 $$:

$$
y - 1 = 1(x - 10)
$$

Simplifying this gives:

$$
y - 1 = x - 10
$$

$$
y = x - 9
$$

Thus, the equation of line $$ w $$ is:

$$
\boxed{y = x - 9}
$$
The equation of line $$ w $$ is $$ y = x - 9 $$.

The equation of line is . Une indudes the point and is
perpendicular to line . What is the equation of line ?

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The equation of line is . Une indudes the point and is perpendicular to line . What is the equation of line ?