Question

Use the graph to answer the question.

A coordinate plane going from negative 5 to 5 in increments of 1 labeled every 5 units on the x axis and from negative 1 to 10 in increments of 1 labeled every 5 units on the y axis with 2 points labeled at left parenthesis 0 comma 8 right parenthesis and at left parenthesis 1 comma 6 right parenthesis. A curve is drawn through the 2 points.


the two marked points are 0,8 and 1, 6


Which equation is shown in the graph?

(1 point)
Responses

y=−8⋅(0.75)x
y is equal to negative 8 times 0 point 7 5 to the x th power

y=(14)x
y is equal to 14 to the x th power

y=8⋅(0.75)x
y is equal to 8 times 0 point 7 5 to the x th power

y=8⋅(1.75)x

Answer 1

To determine which equation represents the curve shown on the graph, we can use the two marked points: (0, 8) and (1, 6).

1. **Plug in the first point (0, 8)** into the equations to check:
- For \(y=−8\cdot(0.75)^x\):
\[
y = -8\cdot(0.75)^0 = -8 \cdot 1 = -8 \quad \text{(not valid, since y should be 8)}
\]
- For \(y=(14)^x\):
\[
y = (14)^0 = 1 \quad \text{(not valid, since y should be 8)}
\]
- For \(y=8\cdot(0.75)^x\):
\[
y = 8\cdot(0.75)^0 = 8\cdot1 = 8 \quad \text{(valid)}
\]
- For \(y=8\cdot(1.75)^x\):
\[
y = 8\cdot(1.75)^0 = 8\cdot1 = 8 \quad \text{(valid)}
\]

2. **Now plug in the second point (1, 6)** into those two valid options to see which one is satisfied:
- For \(y=8\cdot(0.75)^x\):
\[
y = 8\cdot(0.75)^1 = 8\cdot0.75 = 6 \quad \text{(valid)}
\]
- For \(y=8\cdot(1.75)^x\):
\[
y = 8\cdot(1.75)^1 = 8\cdot1.75 = 14 \quad \text{(not valid, since y should be 6)}
\]

Based on these calculations, the equation that matches both points (0, 8) and (1, 6) is:

\[
\boxed{y=8\cdot(0.75)^x}
\]