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A line has a slope of 0 and passes through the point \( (6,15) \). Write its equation in slope- intercept form. Write your answer using integers, proper fractions, and improper fractions in simplest form. Save answer

Ask by West Bright. in the United States
Mar 11,2025

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Tutor-Verified Answer

Answer

The equation of the line is \( y = 15 \).

Solution

1. The slope-intercept form of a line is given by \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept. 2. Since the slope of the line is \( 0 \), we have \( m = 0 \). This tells us that the equation becomes: \[ y = 0 \cdot x + b \quad \text{or simply} \quad y = b. \] 3. The line passes through the point \( (6,15) \). We substitute \( x = 6 \) and \( y = 15 \) into the equation: \[ 15 = b. \] 4. Since \( b = 15 \), the equation of the line in slope-intercept form is: \[ y = 15. \]

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Since the slope is 0, this means the line is horizontal. A horizontal line that passes through the point \( (6,15) \) maintains the \( y \)-value of 15 for all \( x \)-values. Therefore, the equation of the line is \( y = 15 \). In slope-intercept form, this remains just \( y = 15 \), highlighting that no matter what \( x \) you choose, the output will always be 15. So, your answer is \( y = 15 \).

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