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**1. Find the equation of a line having slope `=1/2` and passing through point `A(5,4)`**

**Solution:**

The equation of a line with slope m and passing through `(x_1,y_1)` is `y-y_1=m(x-x_1)`

Putting `(5,4)` for `(x_1,y_1)` and `m=1/2,` we get

`:. y-4=1/2(x-5)`

`:. 2(y-4)=(x-5)`

`:. 2y -8=x -5`

`:. x-2y+3=0`

**2. Find the equation of a line passing through two points `A(3,5)` and `B(6,4)`**

**Solution:**

Here `A(3,5), B(6,4)` are the given points

`:. x_1=3, y_1=5, x_2=6, y_2=4`

The equation of a line AB is

`(y-y_1)/(y_2-y_1)=(x-x_1)/(x_2-x_1)`

`:. (y-5)/(4-5)=(x-3)/(6-3)`

`:. (y-5)/(-1)=(x-3)/(3)`

`:. 3(y-5)=-(x-3)`

`:. 3y -15=-x +3`

`:. x+3y-18=0`

**3. Find the equation of a line having slope `=2` and y intercept `=3`**

**Solution:**

Equation of a line with slope `m` and intercept `c` on Y-axis is `y=mx+c`

Here `m=2` and c=3

`y=2x+3`

`:. 2x-y+3=0`

**4. Find the equation of a line having X-intercept `=3` and Y-intercept `=-5`**

**Solution:**

Here intercept on X-axis `a=3` and Y-intercept `b=-5`

Equation of a line is

`x/a+y/b=1`

`:. x/(3)+y/(-5)=1`

`:. (x)/(3)-(y)/(5)=1`

`:. 5x-3y=15`