Question
Use the information to answer the question.
Information
Function 1 is given by the equation y equals 7 point 5 x plus 2. Function 2 is shown in the table and is linear and continuous.
Function 2
x
y
negative 4
negative 6
negative 2
negative 1
0 4
2
9
4
14
Question
How do the characteristics of the two functions compare? Enter the answers in the boxes.
Response area with 2 text input boxes
The slope of Function 1 is
times the slope of Function 2.
The distance between the y-intercepts of the two functions is
Information
Function 1 is given by the equation y equals 7 point 5 x plus 2. Function 2 is shown in the table and is linear and continuous.
Function 2
x
y
negative 4
negative 6
negative 2
negative 1
0 4
2
9
4
14
Question
How do the characteristics of the two functions compare? Enter the answers in the boxes.
Response area with 2 text input boxes
The slope of Function 1 is
times the slope of Function 2.
The distance between the y-intercepts of the two functions is
Answers
GPT-4o mini
To compare the characteristics of the two functions, we need to determine the slope of Function 1 and Function 2 and the distance between their y-intercepts.
### Function 1:
The equation of Function 1 is given as:
\[ y = 7.5x + 2 \]
- The slope of Function 1 is **7.5**.
- The y-intercept (where x = 0) is **2**.
### Function 2:
To find the slope of Function 2, we can calculate it using the points provided in the table. Here are the points for Function 2:
- (-4, -6)
- (-2, -1)
- (0, 4)
- (2, 9)
- (4, 14)
Let's calculate the slope using two points from the table, for example, the points (0, 4) and (2, 9):
\[
\text{slope} = \frac{y_2 - y_1}{x_2 - x_1} = \frac{9 - 4}{2 - 0} = \frac{5}{2} = 2.5
\]
Now, we can summarize the comparison:
- The slope of Function 1 is **7.5**, and the slope of Function 2 is **2.5**.
- To find how the slope of Function 1 compares to the slope of Function 2:
\[
\frac{7.5}{2.5} = 3
\]
So, the slope of Function 1 is **3 times** the slope of Function 2.
### Distance Between Y-Intercepts:
The y-intercept of Function 1 is **2**. The y-intercept for Function 2 can be directly taken from the table, which is at point (0, 4). So the y-intercept for Function 2 is **4**.
To find the distance between the two y-intercepts:
\[
\text{Distance} = |y_{\text{intercept 1}} - y_{\text{intercept 2}}| = |2 - 4| = 2
\]
### Final Answers:
1. The slope of Function 1 is **3 times** the slope of Function 2.
2. The distance between the y-intercepts of the two functions is **2**.
### Function 1:
The equation of Function 1 is given as:
\[ y = 7.5x + 2 \]
- The slope of Function 1 is **7.5**.
- The y-intercept (where x = 0) is **2**.
### Function 2:
To find the slope of Function 2, we can calculate it using the points provided in the table. Here are the points for Function 2:
- (-4, -6)
- (-2, -1)
- (0, 4)
- (2, 9)
- (4, 14)
Let's calculate the slope using two points from the table, for example, the points (0, 4) and (2, 9):
\[
\text{slope} = \frac{y_2 - y_1}{x_2 - x_1} = \frac{9 - 4}{2 - 0} = \frac{5}{2} = 2.5
\]
Now, we can summarize the comparison:
- The slope of Function 1 is **7.5**, and the slope of Function 2 is **2.5**.
- To find how the slope of Function 1 compares to the slope of Function 2:
\[
\frac{7.5}{2.5} = 3
\]
So, the slope of Function 1 is **3 times** the slope of Function 2.
### Distance Between Y-Intercepts:
The y-intercept of Function 1 is **2**. The y-intercept for Function 2 can be directly taken from the table, which is at point (0, 4). So the y-intercept for Function 2 is **4**.
To find the distance between the two y-intercepts:
\[
\text{Distance} = |y_{\text{intercept 1}} - y_{\text{intercept 2}}| = |2 - 4| = 2
\]
### Final Answers:
1. The slope of Function 1 is **3 times** the slope of Function 2.
2. The distance between the y-intercepts of the two functions is **2**.