Use the graph to answer the question.

Question

(0, 8) (1, 6)

Which equation is shown in the graph?

(1 point)
Responses

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

y=8⋅(0.75)x
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
𝑦
=
8
⋅
(
1.75
)
𝑥
y is equal to 8 times 1 point 7 5 to the x th power

y=(14)x

Answer 1

To determine which equation is shown in the graph with the points (0, 8) and (1, 6), we can analyze the characteristics of these points.

1. The point (0, 8) indicates that when \( x = 0 \), \( y = 8 \). This suggests that the equation has an initial value (y-intercept) of 8.

2. The point (1, 6) indicates that when \( x = 1 \), \( y = 6 \). This suggests that as \( x \) increases from 0 to 1, \( y \) decreases from 8 to 6, indicating a decreasing trend.

Since the points suggest an exponential function with a base less than 1 (to show decay), we can analyze the given options:

Option 1: \( y = -8 \cdot (0.75)^x \)

• This function would yield negative values for \( y \) as \( x \) increases because of the negative coefficient, which does not fit the points given.

Option 2: \( y = 8 \cdot (0.75)^x \)

• At \( x = 0 \): \( y = 8 \cdot (0.75)^0 = 8 \) (this matches).
• At \( x = 1 \): \( y = 8 \cdot (0.75)^1 = 8 \cdot 0.75 = 6 \) (this matches).

Option 3: \( y = 8 \cdot (1.75)^x \)

• This function would yield values increasing exponentially, not fitting the points given.

Option 4: \( y = (14)x \)

• This is a linear equation and does not fit the points provided.

Based on this analysis, the correct answer is:

y = 8 ⋅ (0.75)^x