Question
Consider the linear equation, y = 35x+47
Select all the statement that are true.
(3 points)
Responses
The slope of the line is 47
The slope of the line is 47
The equation 35x − y = 47
is equivalent to the given equation.
The equation 35x − y = 47
is equivalent to the given equation.
The y-intercept for the line is 35
The y-intercept for the line is 35
The y-intercept for the line is 47
The y-intercept for the line is 47
The equation −35x + y = 47
is equivalent to the given equation.
The equation −35x + y = 47
is equivalent to the given equation.
The slope of the line is 35
Select all the statement that are true.
(3 points)
Responses
The slope of the line is 47
The slope of the line is 47
The equation 35x − y = 47
is equivalent to the given equation.
The equation 35x − y = 47
is equivalent to the given equation.
The y-intercept for the line is 35
The y-intercept for the line is 35
The y-intercept for the line is 47
The y-intercept for the line is 47
The equation −35x + y = 47
is equivalent to the given equation.
The equation −35x + y = 47
is equivalent to the given equation.
The slope of the line is 35
Answers
GPT-4o mini
Let's evaluate each statement regarding the linear equation \( y = 35x + 47 \).
1. **The slope of the line is 47**: This statement is **false**. The slope (m) is the coefficient of \( x \), which is 35.
2. **The equation \( 35x − y = 47 \) is equivalent to the given equation.**: To check this, we can rearrange:
\( 35x - y = 47 \) can be rewritten as:
\( y = 35x - 47 \), which is not equivalent to \( y = 35x + 47 \). This statement is **false**.
3. **The y-intercept for the line is 35**: This statement is **false**. The y-intercept (b) is the constant term in the equation when it's in slope-intercept form \( y = mx + b \). Here, \( b = 47 \).
4. **The y-intercept for the line is 47**: This statement is **true**. The y-intercept is indeed 47.
5. **The equation \( -35x + y = 47 \) is equivalent to the given equation.**: To check this, we can rearrange:
\( -35x + y = 47 \) can be rewritten as:
\( y = 35x + 47 \), which is equivalent to the given equation. This statement is **true**.
6. **The slope of the line is 35**: This statement is **true**. The slope of the line is indeed 35.
**In summary, the true statements are:**
- The y-intercept for the line is 47.
- The equation \( -35x + y = 47 \) is equivalent to the given equation.
- The slope of the line is 35.
1. **The slope of the line is 47**: This statement is **false**. The slope (m) is the coefficient of \( x \), which is 35.
2. **The equation \( 35x − y = 47 \) is equivalent to the given equation.**: To check this, we can rearrange:
\( 35x - y = 47 \) can be rewritten as:
\( y = 35x - 47 \), which is not equivalent to \( y = 35x + 47 \). This statement is **false**.
3. **The y-intercept for the line is 35**: This statement is **false**. The y-intercept (b) is the constant term in the equation when it's in slope-intercept form \( y = mx + b \). Here, \( b = 47 \).
4. **The y-intercept for the line is 47**: This statement is **true**. The y-intercept is indeed 47.
5. **The equation \( -35x + y = 47 \) is equivalent to the given equation.**: To check this, we can rearrange:
\( -35x + y = 47 \) can be rewritten as:
\( y = 35x + 47 \), which is equivalent to the given equation. This statement is **true**.
6. **The slope of the line is 35**: This statement is **true**. The slope of the line is indeed 35.
**In summary, the true statements are:**
- The y-intercept for the line is 47.
- The equation \( -35x + y = 47 \) is equivalent to the given equation.
- The slope of the line is 35.