In Exercises 21 to 24, state whether the lines are parallel, perpendicular, the same (coincident), or none of these.
To check:
The relationship between the lines
Initially check the given equation,
If the one equation is derived from other, then these lines are same or coincident in nature.
The two given equations
If not, then proceed with the following procedures.
By theorem,
If two lines are parallel, then their slopes are equal.
(i.e) If
If two lines are perpendicular, then the product of their slopes is
(i.e) If
To find the relation between the lines, the slopes of the lines are needed.
Thus we need to find the points on the lines.
Let
The slope of the line that contains the points
The points of the line
Substitute
On simplifying,
The coefficient of
Thus the first point is
Substitute
The coefficient of
On simplifying,
Thus the second point is
The line
Using slope formula and choosing
Slope
The points of the line
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