A line with a slope of $$ \frac{1}{10} $$ passes through the points $$ (5, t) $$ and $$ (-5,-4) $$. What is the value of $$ t $$ ? $$ t=\square $$

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To find the value of $$ t $$ for the line with a slope of $$ \frac{1}{10} $$ passing through the points $$ (5, t) $$ and $$ (-5, -4) $$, we can use the formula for the slope between two points:

$$
\text{Slope} = \frac{y_2 - y_1}{x_2 - x_1}
$$

Given:
- Point 1: $$ (5, t) $$
- Point 2: $$ (-5, -4) $$
- Slope ($$ m $$): $$ \frac{1}{10} $$

Plugging the values into the slope formula:

$$
\frac{1}{10} = \frac{-4 - t}{-5 - 5}
$$

Simplify the denominator:

$$
\frac{1}{10} = \frac{-4 - t}{-10}
$$

Multiply both sides by $$-10$$ to solve for $$ t $$:

$$
-10 \times \frac{1}{10} = -4 - t
$$

$$
-1 = -4 - t
$$

Add $$ 4 $$ to both sides:

$$
-1 + 4 = -t
$$

$$
3 = -t
$$

Multiply both sides by $$-1$$:

$$
t = -3
$$

$$\boxed{-3}$$
$$ t = -3 $$

A line with a slope of passes through the points and . What is the value of ?

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