Question

How do you find the slope and intercept of $ x = 4 $ ?

Answer 1

Hint: In any linear equation, m is the slope and b is the y-intercept and this equation is known as the slope-intercept equation. Here we are given x-coordinate so y coordinate is equal to zero. Here will find the y intercept value for the standard equation and will also take one example to understand it in the better ways.

Complete step-by-step answer:
Any linear equation has the standard form of
 $ y = mx + b $
Where “m” is the slope of the equation
And “b” is the y=intercept
The slope of the line, “m” can be expressed as
 $ m = \dfrac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}} $ …. (A)
Where $ ({x_1},{y_1}) $ and $ ({x_2},{y_2}) $ are the coordinates of any two points in the given line.
Given that $ x = 4 $ is parallel to the y-axis.
And $ ({x_2} - {x_1} = 0) $ place it in the equation (A)
 $ m = \dfrac{{{y_2} - {y_1}}}{0} $
Any number upon zero is always equal to infinity.
 $ \therefore m = \infty $
The above equation can be re-written as –
 $ \therefore \tan \theta = \infty $
Referring to the trigonometric table-
 $ \therefore \tan \theta = \tan 90^\circ $
Tangents on both the sides of the equation cancel each other.
 $ \Rightarrow \theta = 90^\circ $
Hence, x is the intercept at $ (4,0) $ and it has no y – intercept.

Note: Always remember the standard form of the linear equation, slope and intercept equation as the y intercept depends on the standard equation. Also, know the basic identities to simplify the equation such as zero when multiplied with any number always gives the resultant value as zero.
The property of the slopes of the two perpendicular lines is always equal to $ ( - 1) $ whereas slopes of two parallel lines are always equal to each other.