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CanadaON
Grade 12

Graph and identify properties of horizontal and vertical lines

Lesson

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=22 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

Plot the line $x=-8$x=8 on the number plane.

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QUESTION 2

Find the intersection of the lines $x=6$x=6 and the line $y=-3$y=3 .

QUESTION 3

What is the equation of the line that passes through the point (9,4) and is parallel to the $y$y-axis?

 

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