`0=7y-5x+9`
What are the y-intercept and the slope of the line defined by the equation above?

Options

A. The slope is `-5/7` and the y-intercepts is `-9/7`
B. The slope is `-5/7`, and the y-intercept is `9/7`
C. The slope is `5/7`, and the y-intercept is `-9/7`.
D. The slope is `5/7`, and the y-intercept is `9/7`.

Answer

To find the y-intercept and the slope of the line defined by the equation \(0 = 7y - 5x + 9\), we will convert the equation into the slope-intercept form, which is \(y = mx + c\), where \(m\) is the slope and \(c\) is the y-intercept.

### Step-by-Step Solution:

1. **Start with the given equation:**
\[ 0 = 7y - 5x + 9 \]

2. **Rearrange the equation to isolate \(y\):**
\[ 7y = 5x - 9 \]

3. **Divide every term by 7 to solve for \(y\):**
\[ y = \frac{5}{7}x - \frac{9}{7} \]

4. **Identify the slope and y-intercept:**
- From the equation \(y = \frac{5}{7}x - \frac{9}{7}\):
- The slope \(m\) is \(\frac{5}{7}\)
- The y-intercept \(c\) is \(-\frac{9}{7}\)

### Final Answer:
- **Slope:** \(\frac{5}{7}\)
- **Y-intercept:** \(-\frac{9}{7}\)