Question

The value of m for which \[{\text{3x = y - 8}}\] and \[{\text{6x + my + 16 = 0}}\] coincide is
A.2
B.-2
C.\[\dfrac{1}{2}\]
D.\[ - \dfrac{1}{2}\]

Answer 1

Hint: As the given lines are coinciding which means that both the equations are equal. Means eventually both lines are above each other.

Complete step-by-step answer:
As the equations of both the lines are equal so try to convert line (2) into form of line (1) and compare the coefficients of both the lines . And thus we will get a value of m.
Now, converting line (2)
\[
  {\text{6x + my + 16 = 0}} \\
  {\text{6x = - my - 16}} \\
  {\text{3x = - }}\dfrac{{\text{m}}}{{\text{2}}}{\text{y - 8}} \\
 \]
Now , compare the above line equation with line (1)
So,
\[
  {\text{ - }}\dfrac{{\text{m}}}{{\text{2}}}{\text{ = 1}} \\
  {\text{m = - 2}} \\
 \]
Hence , option (b) is our required answer.

Note: Coincident of line : Two lines or shapes that lie exactly on top of each other. Example: these two lines are coincident, only you can't see them both, because they are on top of each other.
A line is a one-dimensional figure, which has length but no width. A line made of a set of points which is extended in opposite directions infinitely. It is determined by two points in a two-dimensional plane. The two points which lie on the same line are said to be collinear points.
In geometry, there are different types of lines such as horizontal and vertical lines, parallel and perpendicular lines.