Question

Is the line with equation \[y = - 8\], horizontal or vertical?

Answer 1

Hint: To find whether the line with the given equation is horizontal or vertical we will first compare with the standard equation of the line. From comparing we will find the slope of the given line. Then we will use the concept that if the slope is zero then the line is horizontal and if the slope is infinite then the line is vertical. From this concept we will know whether the given line is horizontal or vertical.

Complete step by step answer:
Given equation of the line;
\[y = - 8\]
We can write it as;
\[ \Rightarrow y + 8 = 0\]
Now we know that we can represent a line by the equation as;
\[ \Rightarrow y = mx + c\]
Here, \[m\] is the slope of the line. Now comparing the given equation of line with the standard equation we get \[m\] as zero because the whole \[x\] term is zero. Now since slope is zero this means that the line is parallel to the x-axis and hence a horizontal line.

Therefore, the line with equation \[y = - 8\] is horizontal.

Note: We know that we can also find the slope of a line by differentiating the equation of the line with respect to \[x\]. So, according to that we have;
\[y = - 8\]
Differentiating both sides with respect to \[x\], we get;
\[ \Rightarrow \dfrac{{dy}}{{dx}} = \dfrac{{d\left( { - 8} \right)}}{{dx}}\]
Now we know that the differentiation of the constant is zero. So, we get;
\[ \Rightarrow \dfrac{{dy}}{{dx}} = 0\]
Hence, we can see that the derivative of the given equation of the line is zero with respect to \[x\]. This means that the slope if the line is zero and the line is parallel to the x-axis and hence is a horizontal line.