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A line has a slope of 0 and passes through the point \( (-6,-14) \). Write its equation in slope- intercept form.

Ask by Paul Garrett. in the United States
Dec 11,2024

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Answer

The equation of the line is \( y = -14 \).

Solution

A line with a slope of 0 is a horizontal line. The equation of a horizontal line can be expressed in the form \( y = b \), where \( b \) is the y-coordinate of any point on the line. Since the line passes through the point \( (-6, -14) \), the y-coordinate of this point is \( -14 \). Therefore, the equation of the line is: \[ y = -14 \] This is the equation of the line in slope-intercept form.

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Beyond the Answer

A line with a slope of 0 is a horizontal line, which means it remains constant no matter the value of \( x \). Since it passes through the point \( (-6, -14) \), the \( y \)-value will always be \( -14 \). Therefore, the equation in slope-intercept form is \( y = -14 \). Fun fact: Horizontal lines are like a flat pancake on a plate, staying steady at one height! They can cross the y-axis anywhere, depending only on that constant y-value. In real life, you'll encounter horizontal lines in various scenarios, such as water levels in lakes, the horizon in landscapes, or even while sighting a flight path at cruising altitude. Each displays a constant state or level, much like our equation!

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