Question
Give the slope and the y-intercept of the line with the given equation. Then, graph the linear equation.
y equals 3 x plus 4
Question content area bottom left
Part 1
What is the slope? Select the correct choice below and fill in any answer boxes within your choice.
A.
The slope is
enter your response here.
(Simplify your answer.)
B.
The slope is undefined.
Part 2
What is the y-intercept? Select the correct choice below and fill in any answer boxes within your choice.
A.
The y-intercept is
enter your response here.
y equals 3 x plus 4
Question content area bottom left
Part 1
What is the slope? Select the correct choice below and fill in any answer boxes within your choice.
A.
The slope is
enter your response here.
(Simplify your answer.)
B.
The slope is undefined.
Part 2
What is the y-intercept? Select the correct choice below and fill in any answer boxes within your choice.
A.
The y-intercept is
enter your response here.
Answers
GPT-4o mini
To analyze the linear equation \( y = 3x + 4 \), we can identify the slope and the y-intercept from its standard form.
### Part 1: Slope
The slope-intercept form of a line is given by the equation:
\[ y = mx + b \]
where:
- \( m \) is the slope
- \( b \) is the y-intercept
From the equation \( y = 3x + 4 \):
- The slope \( m \) is **3**.
So the answer for Part 1 is:
- A. The slope is **3**.
### Part 2: Y-Intercept
From the same equation \( y = 3x + 4 \):
- The y-intercept \( b \) is **4**.
So the answer for Part 2 is:
- A. The y-intercept is **4**.
### Graphing the Equation
To graph the equation \( y = 3x + 4 \):
1. Start by plotting the y-intercept at \( (0, 4) \).
2. Use the slope of 3 (which means rise/run = 3/1) to find another point. From \( (0, 4) \), move up 3 units and right 1 unit to get to the point \( (1, 7) \).
3. Draw a line through these points.
This line will extend indefinitely in both directions and will have a positive slope. Here’s a rough sketch of the graph:
```plaintext
|
8| *
7| *
6|
5|
4| *
3|
2|
1|
0|____________________
0 1 2 3 4 5 6
```
- The point \( (0, 4) \) represents the y-intercept.
- The slope indicates the line rises 3 units for every 1 unit it moves to the right.
### Part 1: Slope
The slope-intercept form of a line is given by the equation:
\[ y = mx + b \]
where:
- \( m \) is the slope
- \( b \) is the y-intercept
From the equation \( y = 3x + 4 \):
- The slope \( m \) is **3**.
So the answer for Part 1 is:
- A. The slope is **3**.
### Part 2: Y-Intercept
From the same equation \( y = 3x + 4 \):
- The y-intercept \( b \) is **4**.
So the answer for Part 2 is:
- A. The y-intercept is **4**.
### Graphing the Equation
To graph the equation \( y = 3x + 4 \):
1. Start by plotting the y-intercept at \( (0, 4) \).
2. Use the slope of 3 (which means rise/run = 3/1) to find another point. From \( (0, 4) \), move up 3 units and right 1 unit to get to the point \( (1, 7) \).
3. Draw a line through these points.
This line will extend indefinitely in both directions and will have a positive slope. Here’s a rough sketch of the graph:
```plaintext
|
8| *
7| *
6|
5|
4| *
3|
2|
1|
0|____________________
0 1 2 3 4 5 6
```
- The point \( (0, 4) \) represents the y-intercept.
- The slope indicates the line rises 3 units for every 1 unit it moves to the right.