Horizontal and Vertical Lines II

The line with equation given by $x=a$x=a, with $a$a as any real number, is drawn parallel to the $y$y axis passing through the point $\left(a,0\right)$(a,0) on the $x$x axis.  Three examples, specifically $x=-1$x=−1, $x=1$x=1, and $x=2\sqrt{2}$x=2√2 are shown in the diagram below:

A nice way to think about the line given by the equation $x=a$x=a is to realise that every point on it has the $x$x part of the coordinate address (the abscissae ) as $a$a, and the $y$y part (the ordinate ) completely unrestricted. Thus points like $\left(a,-3\right),\left(a,0\right),\left(a,5\right),\left(a,23\right)$(a,−3),(a,0),(a,5),(a,23) are all on the line, one directly above the other.  Hence, the line is perpendicular to the $x$x-axis.

In a similar way, the line with equation $y=b$y=b, where $b$b is a constant, is parallel to the $x$x-axis and passes through the point $\left(0,b\right)$(0,b) on the $y$y-axis. The lines $y=-3,y=2$y=−3,y=2 and $y=5$y=5 are shown in the following diagram:

Recall the definition of a function. A function is a relation that has the property that each value of the independent variable $x$x is mapped to a unique value of the dependent variable $y$y. This means that the line $x=a$x=a is not a function but the line $y=b$y=b is a function. 

Worked Examples

QUESTION 1

QUESTION 2

QUESTION 3