Question

What is the slope and equation of a line parallel to x-axis and passing through a point $\left( {3,7} \right)$?

Answer 1

In the question we are asked to find the slope as well as the equation of the line passing through a point and parallel to the x-axis. First, we will find the slope of the line. Then to find the equation of the line we will apply the point slope form formula because we know one of the points through which the line passes.

Complete step by step answer:
In the question we have been given that the line is parallel to the x-axis. Now we know that any line parallel to the x-axis will have zero slope. This is because slope is defined as the rate of change of $y$ with respect to $x$, and for a line parallel to x-axis the value of $y$ does not change and hence the slope is zero.
So, we have got the slope, $m = 0$
Now we have one of the points through which the line passes and also the slope of the line. So, we will apply the point slope form. Point slope form states that suppose a line passes through a point $\left( {{x_1},{y_1}} \right)$ and has a slope $m$, then its equation is;
$y - {y_1} = m\left( {x - {x_1}} \right)$
Now we have the point as $\left( {3,7} \right)$, and $m = 0$. So, putting the value we get;
$\Rightarrow y - 7 = 0\left( {x - 3} \right)$
Solving we get;
$\Rightarrow y - 7 = 0$
$\Rightarrow y = 7$
Hence this is the equation of the required line.

Note: One thing we can note is that when a line passes through a point and is parallel to the x-axis then we can simply write the equation of the line by the y-coordinate of the point through which it passes. Similarly, when the line is parallel to the y-axis we can write the equation of the line by the x-coordinate of the point through which it passes.