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Solution
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Solution provided by AtoZmath.com
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Equation of line passing through a given point and parallel to given line calculator
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 1. Find the equation of the line passing through the point `A(5,4)` and parallel to the line `2x+3y+7=0`
2. Find the equation of the line passing through the point `A(1,1)` and parallel to the line `2x-3y+2=0`
3. Find the equation of the line passing through the point `A(2,3)` and parallel to the line `2x-3y+8=0`
4. Find the equation of the line passing through the point `A(2,-5)` and parallel to the line `2x-3y-7=0`
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Example1. 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` 
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