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

To find the value of \( t \), we can use the formula for the slope of a line between two points, which is given by: \[ \text{slope} = \frac{y_2 - y_1}{x_2 - x_1} \] In this case, the two points are \( (5, t) \) and \( (-5, -4) \). We can assign these as follows: - \( (x_1, y_1) = (-5, -4) \) - \( (x_2, y_2) = (5, t) \) The slope is \( \frac{1}{10} \), so we have: \[ \frac{t - (-4)}{5 - (-5)} = \frac{1}{10} \] Simplifying the denominator gives us: \[ \frac{t + 4}{5 + 5} = \frac{t + 4}{10} \] Setting this equal to the slope: \[ \frac{t + 4}{10} = \frac{1}{10} \] Now, we can multiply both sides by 10 to eliminate the fraction: \[ t + 4 = 1 \] Subtracting 4 from both sides results in: \[ t = 1 - 4 = -3 \] Thus, the value of \( t \) is: \[ t = -3 \]