Find the equation of the line whose
(i) slope=3 and y-intercept=5
(ii) slope=-1 and y-intercept=4
(iii) slope =`-(2)/(5)` and y-intercept=-3

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:

\[ y = mx + c \]

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

### Step-by-Step Solution:

**(i)** For the first line:
- Given: Slope \( m = 3 \) and y-intercept \( c = 5 \).
- Substitute \( m \) and \( c \) into the slope-intercept form:
\[ y = 3x + 5 \]

**(ii)** For the second line:
- Given: Slope \( m = -1 \) and y-intercept \( c = 4 \).
- Substitute \( m \) and \( c \) into the slope-intercept form:
\[ y = -1x + 4 \quad \text{or} \quad y = -x + 4 \]
- We can rearrange this to standard form:
\[ x + y = 4 \]

**(iii)** For the third line:
- Given: Slope \( m = -\frac{2}{5} \) and y-intercept \( c = -3 \).
- Substitute \( m \) and \( c \) into the slope-intercept form:
\[ y = -\frac{2}{5}x - 3 \]
- To convert this to standard form, we can multiply through by 5 to eliminate the fraction:
\[ 5y = -2x - 15 \]
- Rearranging gives:
\[ 2x + 5y + 15 = 0 \]

### Summary of Equations:
1. For slope = 3 and y-intercept = 5:
\[ y = 3x + 5 \]
2. For slope = -1 and y-intercept = 4:
\[ x + y = 4 \]
3. For slope = -\(\frac{2}{5}\) and y-intercept = -3:
\[ 2x + 5y + 15 = 0 \]