Question

Function 1 is defined by the equation y = 4x - 5, and the function 2 is represented by the graph below.



Which statement about the function is true?
Responses
A Function 2 has the greater rate of change, and function 1 has the greater y-intercept.Function 2 has the greater rate of change, and function 1 has the greater y -intercept.
B Function 2 has the greater rate of change and the greater y-intercept.Function 2 has the greater rate of change and the greater y -intercept.
C Function 1 has the greater rate of change and the greater y-intercept.Function 1 has the greater rate of change and the greater y -intercept.
D Function 1 has the greater rate of change, and function 2 has the greater y-intercept.

Answer 1

To determine which statement about the functions is true, we need to analyze the rate of change (slope) and y-intercept of both function 1 and function 2.

Function 1 is given by the equation:
\[ y = 4x - 5 \]
From this equation:
- The slope (rate of change) is 4.
- The y-intercept is -5 (the value of y when x = 0).

For function 2, we would need to examine its graph to determine its slope and y-intercept. However, since the graph is not provided here, I will explain how to analyze it:

1. **Rate of Change (Slope) of Function 2**:
- Determine two points on the graph of function 2 to calculate its slope using the formula:
\[ \text{slope} = \frac{y_2 - y_1}{x_2 - x_1} \]
- Compare this slope to the slope of function 1, which is 4.

2. **Y-Intercept of Function 2**:
- Read the y-coordinate of the point where function 2 crosses the y-axis (x = 0).
- Compare this value to -5, the y-intercept of function 1.

Once you have both slopes and y-intercepts, you can compare them to figure out which statement is true based on the options provided.

### Without the graph of Function 2:
- If function 2 has a slope greater than 4, then it has the greater rate of change.
- If function 2's y-intercept is greater than -5, then it has the greater y-intercept.

### Based on available choices:
- A and D state that function 1 has the greater y-intercept.
- B states that function 2 has the greater y-intercept.
- C states that function 1 has both the greater rate of change and the greater y-intercept.

Therefore, the comparison depends on the specific slope and y-intercept of function 2. You must check the graph for these values to select the correct statement. If you can provide the graph or key points from it, I can assist with identifying the accurate answer!