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------------------------------------------------ Given that [tex]$L_1$[/tex] is parallel to the [tex]$x$[/tex]-axis, write down the equation of [tex]$L_1$[/tex].

(Note: [tex]$L_1$[/tex] is parallel to the [tex]$x$[/tex]-axis and passes through the point [tex]$A$[/tex] at [tex]$(0,4)$[/tex].)

Answer :

Since [tex]$L_1$[/tex] is parallel to the [tex]$x$[/tex]-axis, it is a horizontal line. A horizontal line has a constant [tex]$y$[/tex]-coordinate for all values of [tex]$x$[/tex].

Because [tex]$L_1$[/tex] passes through the point [tex]$A(0,4)$[/tex], the constant [tex]$y$[/tex]-coordinate is [tex]$4$[/tex].

Thus, the equation of [tex]$L_1$[/tex] is:

[tex]$$
y = 4
$$[/tex]

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