Question

1. fill in the missing coordinate in each ordered pair so that the pair is a solution of $y = -3^x$. 11b \\(\left( -2, -\frac{1}{9} \

ight)\\) 5 you got it! 11c \\(\left( -1, -\frac{1}{3} \
ight)\\) 5 nailed it! 11d \\(\left( \square, -243 \
ight)\\)

Explanation:

Step1: Substitute y into the equation

We know the equation is \( y = -3^x \), and we are given \( y = -243 \). So we substitute \( y \) into the equation:
\( -243 = -3^x \)

Step2: Simplify the equation

Divide both sides of the equation by -1:
\( 243 = 3^x \)

Step3: Recall the power of 3

We know that \( 3^5 = 243 \) (because \( 3\times3\times3\times3\times3 = 243 \)). So we have:
\( 3^5 = 3^x \)

Step4: Solve for x

Since the bases are the same, the exponents must be equal. So \( x = 5 \).

Answer:

5