Question

How do you find the slope of a line $y = 5$ ?

Answer 1

The slope of a line in graph is the $\tan$ of the angle made by the line with the x-axis. In other words, it is the change in the value of $y$ with respect to $x$ in the equation. For a straight line, if two points $A({x_1},{\kern 1pt} {\kern 1pt} {\kern 1pt} {y_1})$ and $B({x_2},{\kern 1pt} {\kern 1pt} {\kern 1pt} {y_2})$ are situated on the line, then by slope formula we can calculate the slope (m) as, $m = \dfrac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}}$ . Alternatively, we can also find the slope of the line by using the slope-intercept formula wherein we write the given equation in the form $y = mx + c$ , where $m$ is the slope of the line and $c$ is the y-intercept.

Complete step by step solution:
We have to find the slope of the line given by the equation $y = 5$ .
We will use the slope-intercept formula to find the slope of the line.
The slope-intercept formula is given by $y = mx + c$ .
We can rewrite the given equation in the form,
$y = 5 \\\ \Rightarrow y = (0 \times x) + 5 \\\$
On comparing with the standard form of the slope-intercept formula, we see that
$m = 0$ and $c = 5$
Thus, the slope of the given line is $0$ and the y-intercept is $5$ .
We can observe that the line $y = 5$ is a straight line parallel to x-axis, i.e. for any change in the value of $x$ , the value of $y$ does not change. So the slope is $0$ .

Hence, the slope of the line $y = 5$ is $0$ .

Note: For a horizontal line parallel to x-axis, the slope is $0$ as the value of $y$ does not change for any change in the value of $x$ . We will arrive at the same result if we use the slope formula $m = \dfrac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}}$ to find the slope using any two points on the line.