Find the slope and the y-intercept of the line:
(i) `2x-3y+5=0` (ii) `2y+5x=7` (iii) `2y-5=0`

Answer

To find the slope and the y-intercept of the given lines, we will convert each equation into the slope-intercept form, which is given by:

\[ y = mx + c \]

where \( m \) is the slope and \( c \) is the y-intercept.

### (i) For the equation \( 2x - 3y + 5 = 0 \):

1. **Rearrange the equation**: Start by isolating \( y \).
\[ 2x - 3y + 5 = 0 \implies -3y = -2x - 5 \]

2. **Divide by -3**:
\[ y = \frac{2}{3}x + \frac{5}{3} \]

3. **Identify slope and y-intercept**: From the equation \( y = \frac{2}{3}x + \frac{5}{3} \), we can see that:
- Slope \( m = \frac{2}{3} \)
- y-intercept \( c = \frac{5}{3} \)

### (ii) For the equation \( 2y + 5x = 7 \):

1. **Rearrange the equation**: Isolate \( y \).
\[ 2y = -5x + 7 \]

2. **Divide by 2**:
\[ y = -\frac{5}{2}x + \frac{7}{2} \]

3. **Identify slope and y-intercept**: From the equation \( y = -\frac{5}{2}x + \frac{7}{2} \), we find:
- Slope \( m = -\frac{5}{2} \)
- y-intercept \( c = \frac{7}{2} \)

### (iii) For the equation \( 2y - 5 = 0 \):

1. **Rearrange the equation**: Isolate \( y \).
\[ 2y = 5 \]

2. **Divide by 2**:
\[ y = 0x + \frac{5}{2} \]

3. **Identify slope and y-intercept**: From the equation \( y = 0x + \frac{5}{2} \), we see:
- Slope \( m = 0 \)
- y-intercept \( c = \frac{5}{2} \)

### Final Results:
- For \( 2x - 3y + 5 = 0 \): Slope = \( \frac{2}{3} \), y-intercept = \( \frac{5}{3} \)
- For \( 2y + 5x = 7 \): Slope = \( -\frac{5}{2} \), y-intercept = \( \frac{7}{2} \)
- For \( 2y - 5 = 0 \): Slope = \( 0 \), y-intercept = \( \frac{5}{2} \)