Find the slope and y-intercept of the st.line in each of the following :
`(i) x+y=0` `(ii) y+2=0`
`(iii) (y)/(x)=2` `(iv)5x+6y=7`

Answer

To find the slope and y-intercept of the given straight lines, we will convert each equation into the slope-intercept form, which is \(y = mx + c\), where \(m\) is the slope and \(c\) is the y-intercept.

### (i) For the equation \(x + y = 0\):

1. **Rearrange the equation** to isolate \(y\):
\[ y = -x \]

2. **Identify the slope and y-intercept**:
- Slope \(m = -1\)
- Y-intercept \(c = 0\)

**Final answer for (i)**: Slope = \(-1\), Y-intercept = \(0\)

### (ii) For the equation \(y + 2 = 0\):

1. **Rearrange the equation** to isolate \(y\):
\[ y = -2 \]

2. **Identify the slope and y-intercept**:
- Slope \(m = 0\) (since there is no \(x\) term)
- Y-intercept \(c = -2\)

**Final answer for (ii)**: Slope = \(0\), Y-intercept = \(-2\)

### (iii) For the equation \(\frac{y}{x} = 2\):

1. **Multiply both sides by \(x\)** to eliminate the fraction:
\[ y = 2x \]

2. **Identify the slope and y-intercept**:
- Slope \(m = 2\)
- Y-intercept \(c = 0\)

**Final answer for (iii)**: Slope = \(2\), Y-intercept = \(0\)

### (iv) For the equation \(5x + 6y = 7\):

1. **Rearrange the equation** to isolate \(y\):
\[ 6y = -5x + 7 \]
\[ y = -\frac{5}{6}x + \frac{7}{6} \]

2. **Identify the slope and y-intercept**:
- Slope \(m = -\frac{5}{6}\)
- Y-intercept \(c = \frac{7}{6}\)

**Final answer for (iv)**: Slope = \(-\frac{5}{6}\), Y-intercept = \(\frac{7}{6}\)

### Summary of Answers:
1. (i) Slope = \(-1\), Y-intercept = \(0\)
2. (ii) Slope = \(0\), Y-intercept = \(-2\)
3. (iii) Slope = \(2\), Y-intercept = \(0\)
4. (iv) Slope = \(-\frac{5}{6}\), Y-intercept = \(\frac{7}{6}\)