Graphing Horizontal Lines

Horizontal lines have zero slope. To graph a horizontal line in the standard coordinate system, use the equation $y = k ,$ where $k$ gives the point on the $y$-axis that the line will intersect.

The slope of a line can be described as the ratio of a line's "rise" to its "run." The slope of a horizontal line is 0 because it has zero rise for any amount of run and zero divided by any number equals zero.

Suppose we want a horizontal line that passes through $(0,5) .$

In addition to that point, the line will pass through

$$\ldots, (-3, 5), (-2, 5), (-1, 5), (1, 5), (2, 5), (3, 5), \ldots$$

and in general for any real number $Q,$ the graph will pass through $(Q, 5) .$

This means the $x$-coordinate can vary to any real number, so it doesn't get fixed at all and doesn't need to appear in the horizontal line equation. $y$ on the other hand must always be 5, giving an equation of $y = 5 .$

Note that if we attempt to use a traditional line form, like the slope-intercept form $y = mx + b ,$ we create a line with the equation $y=0x+b,$ or $y=b,$ where $b$ is the $y$-intercept of the line.

What is the equation of the line that passes through the points $(5, 4)$ and $(-2,4)\,?$

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ANSWER

Because both of the points on the line have a $y$-value of 4, every point on the line will have a $y$-value of 4 and the equation of the horizontal line is $y=4.$