To find the equation of line \( t \), which is parallel to line \( s \), we need to identify the slope of line \( s \) from its equation and then use that same slope for line \( t \).
The equation of line \( s \) is given as:
\[ y = -10x + \frac{5}{4} \]
From this equation, we can see that the slope (\( m \)) of line \( s \) is \( -10 \).
Since line \( t \) is parallel to line \( s \), it will have the same slope. Therefore, line \( t \) also has a slope of \( -10 \).
Next, we use the point through which line \( t \) passes, which is \((-1, 3)\), to write the equation of line \( t \) using point-slope form:
\[ y - y_1 = m(x - x_1) \]
Substituting in the values for \( m \), \( x_1 \), and \( y_1 \):
\[ y - 3 = -10(x - (-1)) \] \[ y - 3 = -10(x + 1) \]
Now, let's simplify this equation:
\[ y - 3 = -10x - 10 \] \[ y = -10x - 10 + 3 \] \[ y = -10x - 7 \]
Thus, the equation of line \( t \) in slope-intercept form is:
\[ \boxed{y = -10x - 7} \]