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 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 35
The slope of the line is 35

The equation 35x − y = 47
is equivalent to the given equation.

Answer 1

Let's analyze the linear equation: \( y = 35x + 47 \).

1. **The slope of the line is 47** - **False**. The slope (m) is the coefficient of \(x\), which is 35 in this case.

2. **The slope of the line is 47** - **False** (same reason as above).

3. **The y-intercept for the line is 35** - **False**. The y-intercept (b) is the constant term in the equation, which is 47.

4. **The y-intercept for the line is 35** - **False** (same reason as above).

5. **The y-intercept for the line is 47** - **True**. The y-intercept is indeed 47.

6. **The slope of the line is 35** - **True**. The slope is 35 as it is the coefficient of \(x\).

7. **The equation −35x + y = 47 is equivalent to the given equation** - **True**. This can be rearranged to the slope-intercept form \(y = 35x + 47\) by adding \(35x\) to both sides.

8. **The equation 35x − y = 47 is equivalent to the given equation** - **False**. This can be rearranged to the form \(y = 35x - 47\), which is not equivalent to \(y = 35x + 47\).

In summary, the true statements are:

- The y-intercept for the line is 47.
- The slope of the line is 35.
- The equation −35x + y = 47 is equivalent to the given equation.