Is the line with equation y = -8 horizontal or vertical?

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Answer 1 · 2015-08-14T20:19:51

Horizontal.

Think of what you've got here.

You know that the equation of a line in slope-intercept form is

$y = m x + b$ $color(blue)(y = mx + b)$ , where

$m$ $m$ - the sloper of the line;
$b$ $b$ - the coordinate of the $y$ $y$ -intercept on the $y$ $y$ -axis.

Now, the equation for your line looks like this

$y = - 8$ $y = -8$

Notice that it's missing the $x$ $x$ -term. This means that the slope of the line must be equal to zero.

What this tells you is that for any value of $x$ $x$ , the line will intersect the $y$ $y$ -axis in the exact same place, $- 8$ $-8$ .

Therefore, the line described by the equation $y = - 8$ $y = -8$ must be horizontal.

graph{y + 8 = 0.001x [-13.17, 12.15, -11.11, 1.54]}