1. Find the equation of the line passing through the point `A(5,4)` and parallel to the line `2x+3y+7=0`Solution:Here Point `(x_1,y_1)=(5,4)` and line `2x+3y+7=0` (given)
When two lines are parallel, their slopes are equal.
We shall first find the slope of line `2x+3y+7=0`
`2x+3y+7=0`
`:. 3y=-2x-7`
`:. y=-(2x)/(3)-7/3`
`:.` Slope `=-2/3` and hence slope of the line parallel to this line is also `-2/3`
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)=(5,4)` and Slope `m=-2/3` (given)
`:. y-4=-2/3(x-5)`
`:. 3(y-4)=-2(x-5)`
`:. 3y -12=-2x +10`
`:. 2x+3y-22=0`
Hence, The equation of line is `2x+3y-22=0`
2. Find the equation of the line passing through the point `A(1,1)` and parallel to the line `2x-3y+2=0`Solution:Here Point `(x_1,y_1)=(1,1)` and line `2x-3y+2=0` (given)
When two lines are parallel, their slopes are equal.
We shall first find the slope of line `2x-3y+2=0`
`2x-3y+2=0`
`:. 3y=2x+2`
`:. y=(2x)/(3)+2/3`
`:.` Slope `=2/3` and hence slope of the line parallel to this line is also `2/3`
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)=(1,1)` and Slope `m=2/3` (given)
`:. y-1=2/3(x-1)`
`:. 3(y-1)=2(x-1)`
`:. 3y -3=2x -2`
`:. 2x-3y+1=0`
Hence, The equation of line is `2x-3y+1=0`
3. Find the equation of the line passing through the point `A(2,3)` and parallel to the line `2x-3y+8=0`Solution:Here Point `(x_1,y_1)=(2,3)` and line `2x-3y+8=0` (given)
When two lines are parallel, their slopes are equal.
We shall first find the slope of line `2x-3y+8=0`
`2x-3y+8=0`
`:. 3y=2x+8`
`:. y=(2x)/(3)+8/3`
`:.` Slope `=2/3` and hence slope of the line parallel to this line is also `2/3`
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=2/3` (given)
`:. y-3=2/3(x-2)`
`:. 3(y-3)=2(x-2)`
`:. 3y -9=2x -4`
`:. 2x-3y+5=0`
Hence, The equation of line is `2x-3y+5=0`
4. Find the equation of the line passing through the point `A(2,-5)` and parallel to the line `2x-3y-7=0`Solution:Here Point `(x_1,y_1)=(2,-5)` and line `2x-3y-7=0` (given)
When two lines are parallel, their slopes are equal.
We shall first find the slope of line `2x-3y-7=0`
`2x-3y-7=0`
`:. 3y=2x-7`
`:. y=(2x)/(3)-7/3`
`:.` Slope `=2/3` and hence slope of the line parallel to this line is also `2/3`
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,-5)` and Slope `m=2/3` (given)
`:. y+5=2/3(x-2)`
`:. 3(y+5)=2(x-2)`
`:. 3y +15=2x -4`
`:. 2x-3y-19=0`
Hence, The equation of line is `2x-3y-19=0`
This material is intended as a summary. Use your textbook for detail explanation.
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