Question
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
Upstudy AI Solution
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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Extra Insights
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 \( y = 15 \).