To find the y-value when \( x = -6 \) for the function \( y = 3(5)^x \), we can substitute \( x \) into the equation.
\[ y = 3(5)^{-6} \]
Now, calculate \( (5)^{-6} \):
\[ (5)^{-6} = \frac{1}{(5)^6} \]
Now calculate \( (5)^6 \):
\[ (5)^6 = 15625 \]
Thus,
\[ (5)^{-6} = \frac{1}{15625} \]
Substituting back into the equation for \( y \):
\[ y = 3 \times \frac{1}{15625} = \frac{3}{15625} \]
Therefore, the y-value when \( x = -6 \) is:
\[ \left(-6, \frac{3}{15625}\right) \]
In decimal form, \( \frac{3}{15625} \) is approximately \( 0.000192 \).
So the final coordinates are:
\[ \left(-6, \frac{3}{15625}\right) \quad \text{or approximately} \quad \left(-6, 0.000192\right) \]