Question

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

Answer 1

Hint: 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.