Question

Consider the linear equation, y = 35x+47

Select all the statement that are true.

(3 points)
Responses

The y-intercept for the line is 47
The y-intercept for the line is 47

The slope of the line is 35
The slope of the line is 35

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 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 47

Answer 1

Let's analyze each statement based on the given linear equation \( y = 35x + 47 \):

1. **The y-intercept for the line is 47**:
- **True**. In the equation \( y = mx + b \), \( b \) represents the y-intercept. Here, \( b = 47 \).

2. **The slope of the line is 35**:
- **True**. In the equation \( y = mx + b \), \( m \) represents the slope. Here, \( m = 35 \).

3. **The equation \( 35x - y = 47 \) is equivalent to the given equation**:
- **True**. Rewriting the original equation \( y = 35x + 47 \) in standard form gives us:
\[
35x - y = -47 \quad \text{(this is not what we have)}
\]
The correct form of the equation that represents the same line requires additional manipulation. Thus, the claim that it's equivalent is **False**.

4. **The y-intercept for the line is 35**:
- **False**. As mentioned earlier, the y-intercept is 47, not 35.

5. **The equation \( -35x + y = 47 \) is equivalent to the given equation**:
- **True**. If we rearrange \( -35x + y = 47 \), we can rewrite it as \( y = 35x + 47 \).

6. **The slope of the line is 47**:
- **False**. The slope is 35, not 47.

In summary, the true statements are:
1. The y-intercept for the line is 47
2. The slope of the line is 35
5. The equation \( -35x + y = 47 \) is equivalent to the given equation.