Question

Find the equation of the line parallel to the line 3x - 4y+ 2 is equal to zero and passing through the points (-2,3)

Answer 1

For a straight line having the equation $Ax+By+C=0,$ the slope, we know, is given by,

$m=-\dfrac {A}{B}$

In the case of parallel lines, the slopes are equal. Thus the parallel lines are in the form,

$Ax+By+k=0,\quad\forall k\in\mathbb{R}$

Thus, our answer should be in the form 3x - 4y + k = 0 since it is parallel to the line 3x - 4y + 2 = 0

3x - 4y + k = 0 → (1)

Now we have to find the value of k.

Since (-2, 3) is a point on this line, let x = -2 and y = 3. Then (1) becomes,

3(-2) - 4(3) + k = 0

- 6 - 12 + k = 0

k = 18

Therefore, the equation of the line parallel to the line 3x - 4y + 2 = 0 and passing through the point (-2, 3) is 3x - 4y + 18 = 0.

#answerwithquality

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