Question

Two lines are parallel if and only if their slopes are:
A) Equal
B) Unequal
C) Does not exist
D) Perpendicular

Answer 1

Hint: We are asked the relation between the slopes of two parallel lines or what must be the relation between the slopes of two lines so that they can be parallel. Lines that do not intersect each other and have a constant perpendicular between them are called parallel lines. We will use the concept of parallel lines and how they can be parallel. Parallel lines and slopes are easy Parallel lines and their slopes are easy. Since slope is a measure of the angle of a line from the horizontal and sis Parallel Lines was at the same angles and parallel lines have the same stroke and the lines with the same slopes are parallel.
For example if we are given a slope $m_1$$={\displaystyle \frac{3}{5}}$ and $m_2$$={\displaystyle \frac{3}{5}}$ and both have same slopes then we can say that these must be a slopes of a parallel lines.

Complete step-by-step solution:
Step1: Two lines are parallel if and if only their slopes are:
Equal
Note that two lines are parallel if their slopes are equal and they have different Y intercept parallel lines are two lines in a plane that will never intersect (meaning they will continue on forever without ever touching) a key feature of parallel lines is that they have identical slopes. The Slope of a line is defined as the rise (change in $$Y$$ coordinates over the run (change in $$x$$ -coordinates) of a line in other words how steep the line is. If the line is parallel lines are most commonly represented by a vertical lines for example, $$AB||CD$$ indicates that line $$AB$$ is parallel to $$CD$$.

Option A is the correct answer.

Note: In such types of questions no calculations are required. These questions are based on the properties of the particular topic. If we applied the properties correctly the question will never be long before doing such a question. Always take quick revision of properties than solve the questions. In case of finding slope only slope of parallel lines and perpendicular lines are interconnected one having similar slope while the other have reciprocal with opposite sign with each other.