Find the equation of a line whose
(i) slope =-3 and y-intercept =5 (ii) m=8 and c=-6

Answer

To find the equations of the lines based on the given slopes and y-intercepts, we will use the slope-intercept form of the equation of a line, which is given by:

\[ y = mx + c \]

where:
- \( m \) is the slope of the line,
- \( c \) is the y-intercept.

### (i) For the first line:
1. **Identify the slope and y-intercept**:
- Slope \( m = -3 \)
- y-intercept \( c = 5 \)

2. **Substitute the values into the slope-intercept form**:
\[ y = mx + c \implies y = -3x + 5 \]

3. **Rearranging to standard form**:
- To express it in standard form \( Ax + By + C = 0 \):
\[ y + 3x - 5 = 0 \implies 3x + y - 5 = 0 \]

### (ii) For the second line:
1. **Identify the slope and y-intercept**:
- Slope \( m = 8 \)
- y-intercept \( c = -6 \)

2. **Substitute the values into the slope-intercept form**:
\[ y = mx + c \implies y = 8x - 6 \]

3. **Rearranging to standard form**:
- To express it in standard form \( Ax + By + C = 0 \):
\[ y - 8x + 6 = 0 \implies -8x + y + 6 = 0 \implies 8x - y - 6 = 0 \]

### Final Equations:
- For the first line: \( 3x + y - 5 = 0 \)
- For the second line: \( 8x - y - 6 = 0 \)