Question

The graph is in a downward slope there's a point at negative 1, 10 and another point at one, 3.6 which equation is shown in the graft y = 6 * 0.6 X y = 6 * 3.6 x y = 10 * 1.05 x y = 6 * 0.6 X

Answer 1

To determine which of the given equations corresponds to the graph with the points (−1, 10) and (1, 3.6), we can evaluate each equation using those points.

1. **For the equation \(y = 6 \times 0.6^x\):**

- For \(x = -1\):
\[
y = 6 \times 0.6^{-1} = 6 \times \frac{1}{0.6} = 6 \times \frac{10}{6} = 10 \quad (\text{this point is correct})
\]

- For \(x = 1\):
\[
y = 6 \times 0.6^1 = 6 \times 0.6 = 3.6 \quad (\text{this point is also correct})
\]

2. **For the equation \(y = 6 \times 3.6^x\):**

- For \(x = -1\):
\[
y = 6 \times 3.6^{-1} = 6 \times \frac{1}{3.6} \approx 1.67 \quad (\text{this point does not match})
\]

3. **For the equation \(y = 10 \times 1.05^x\):**

- For \(x = -1\):
\[
y = 10 \times 1.05^{-1} = 10 \times \frac{1}{1.05} \approx 9.52 \quad (\text{this point does not match})
\]

4. **The last equation \(y = 6 \times 0.6^x\)** is already checked.

Based on the calculations, the correct equation that corresponds to the points \((-1, 10)\) and \( (1, 3.6)\) is:

\[
y = 6 \times 0.6^x
\]