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8. A line has a slope of 0 and a \( y \)-intercept of -16 . Write its equation in slope-intercept form. Write your answer using integers, proper fractions, and improper fractions in simplest form.

Ask by Simmons Rogers. in the United States
Jan 31,2025

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Answer

The equation of the line is \( y = -16 \).

Solution

The slope-intercept form of a line is given by: \[ y = mx + b \] where: - \( m \) is the slope - \( b \) is the \( y \)-intercept Given: - Slope (\( m \)) = 0 - \( y \)-intercept (\( b \)) = -16 Substituting these values into the slope-intercept form: \[ y = 0x - 16 \] Since \( 0x \) equals 0, the equation simplifies to: \[ y = -16 \] **Final Answer:** \[ y = -16 \]

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Bonus Knowledge

The equation of a line in slope-intercept form is given by \( y = mx + b \), where \( m \) is the slope and \( b \) is the \( y \)-intercept. Since the slope is 0, the equation simplifies to \( y = 0x - 16 \). This can be further simplified to \( y = -16 \). So, the equation is simply \( y = -16 \). This equation represents a horizontal line that crosses the \( y \)-axis at -16 and runs parallel to the \( x \)-axis. Every point on this line has a \( y \)-coordinate of -16, regardless of the \( x \)-coordinate. If you're ever graphing this line, just remember; it's as flat as a pancake! As you plot, you'll quickly notice how it doesn't tilt or rise at all, creating a perfect horizontal line across your graph. Every point on this line has the same \( y \)-value, proving that not all lines have to be dramatic—some can just chill!

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