1. Find the equation of a straight line passing through `A(-4,5)` and having slope `-2/3`
Solution:
The equation of a line with slope m and passing through `(x_1,y_1)` is `y-y_1=m(x-x_1)`
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`
2. Find the equation of a straight line passing through `A(4,5)` and having slope `1`
Solution:
The equation of a line with slope m and passing through `(x_1,y_1)` is `y-y_1=m(x-x_1)`
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`
3. Find the equation of a straight line passing through `A(-2,3)` and having slope `-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)`
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`
4. Find the equation of a straight line passing through `A(-1,2)` and having slope `-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)`
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`
This material is intended as a summary. Use your textbook for detail explanation.
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