Question

How do you write an equation of a line that is parallel to another?

Answer 1

In this question we have to write an equation of a line that is parallel to another parallel lines are the lines that never intersect each other. So, a pair of parallel lines have equal slopes. The slope of a line shows how slant the line is. It is denoted by the symbol $m$. It is the ratio of change in $y$ to the change in $x$ along the line.

Complete step by step solution:
To write the equation of parallel we must need to know what is the equation of a line. The equation of a straight line is $y = mx + c$. It has a slope of $m$ and makes an intercept of $c$ on the $y$ - axis. This equation is called slope- intercept form.
So, to find an equation of a line that is parallel to another, we have to make sure that their slopes must be equal.
Therefore, we can write the equation of parallel lines as
$\Rightarrow y = mx + b$
$\Rightarrow y = mx + c$
For parallel lines, slopes must be equal. In the above equation $m$ is a slope of a line, $b$ and $c$ are constants. Note that they have to be different, if they are equal then we have two identical lines and they will intersect each other at some point.
Therefore, the above two lines are parallel lines.

Note:
If two lines are parallel then their slopes must be equal but their intercepts should be different. If they had the same intercepts, they would be identical lines. Note that when the slopes of two lines are equal then they are parallel lines and when the product of both the slopes is equal to $- 1$ then the two lines are perpendicular to each other.