1. Find the equation of a straight line passing through `A(-4,5)` and having slope `-2/3`

Solution:


Here Point `(x_1,y_1)=(-4,5)` and Slope `m=-2/3` (given)

`:. y-5=-2/3(x+4)`

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

`:. 3y -15=-2x -8`

`:. 2x+3y-7=0`

Hence, The equation of line is `2x+3y-7=0`

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

Solution:


Here Point `(x_1,y_1)=(4,5)` and Slope `m=1` (given)

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

`:. y -5=x -4`

`:. x-y+1=0`

Hence, The equation of line is `x-y+1=0`

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3. Find the equation of a straight line passing through `A(-2,3)` and having slope `-4`

Solution:


Here Point `(x_1,y_1)=(-2,3)` and Slope `m=-4` (given)

`:. y-3=-4(x+2)`

`:. y -3=-4x -8`

`:. 4x+y+5=0`

Hence, The equation of line is `4x+y+5=0`

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

Solution:


Here Point `(x_1,y_1)=(-1,2)` and Slope `m=-5/4` (given)

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

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

`:. 4y -8=-5x -5`

`:. 5x+4y-3=0`

Hence, The equation of line is `5x+4y-3=0`