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

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 slope of the line is 35

Answer 1

Let's evaluate the statements one by one based on the given linear equation \( y = 35x + 47 \).

1. **The y-intercept for the line is 35.**
**False**. The y-intercept is the value of \( y \) when \( x = 0 \). In this equation, substituting \( x = 0 \) gives \( y = 47 \). So, the y-intercept is 47, not 35.

2. **The equation \(-35x + y = 47\) is equivalent to the given equation.**
**False**. To check this, we can rearrange \(-35x + y = 47\). Adding \(35x\) to both sides gives \(y = 35x + 47\), which is the original equation. Thus, the statement is true as it is equivalent.

3. **The y-intercept for the line is 47.**
**True**. As derived earlier, the y-intercept when \( x = 0 \) is indeed \( y = 47 \).

4. **The slope of the line is 47.**
**False**. The slope of the line is the coefficient of \( x \) in the standard form \( y = mx + b \), where \( m \) is the slope. Here, the slope is 35, not 47.

5. **The equation \( 35x - y = 47 \) is equivalent to the given equation.**
**True**. We can rearrange \( 35x - y = 47 \) by isolating \( y \) to get \( y = 35x - 47 \). This is not the same as the original equation, so the statement is false.

6. **The slope of the line is 35.**
**True**. The slope of the line (\( m \)) from the equation \( y = 35x + 47 \) is indeed 35.

### Summary of True Statements:
- The equation \(-35x + y = 47\) is equivalent to the given equation. (True)
- The y-intercept for the line is 47. (True)
- The slope of the line is 35. (True)

### Final Selections:
- The equation \(-35x + y = 47\) is equivalent to the given equation.
- The y-intercept for the line is 47.
- The slope of the line is 35.