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Score: \( 6 / 10 \) Penalty: none Question What is the equation of the line that passes through the point \( (-6,4) \) and has a slope of 0 ? Answer Attempt 1 out of 3
Ask by Turnbull West. in the United States
Feb 21,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The equation of the line is \( y = 4 \).
Solution
To find the equation of a line that passes through a specific point and has a given slope, we can use the point-slope form of the equation of a line, which is given by:
\[
y - y_1 = m(x - x_1)
\]
where:
- \( (x_1, y_1) \) is a point on the line,
- \( m \) is the slope of the line.
In this case, we have:
- The point \( (-6, 4) \) which gives us \( x_1 = -6 \) and \( y_1 = 4 \).
- The slope \( m = 0 \).
Now, substituting these values into the point-slope form:
\[
y - 4 = 0(x + 6)
\]
Since the slope \( m = 0 \), the equation simplifies to:
\[
y - 4 = 0
\]
This means:
\[
y = 4
\]
Thus, the equation of the line that passes through the point \( (-6, 4) \) and has a slope of 0 is:
\[
\boxed{y = 4}
\]
This represents a horizontal line at \( y = 4 \).
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Simplify this solution Mind Expander
When a line has a slope of 0, it means that it is perfectly horizontal. This means that the y-coordinate remains constant regardless of the x-coordinate. Since the line passes through the point \((-6, 4)\), the equation of the line would be \(y = 4\). This tells us that no matter where you’re at along the x-axis, the value of y will always be 4! Think about a flat horizon—this line essentially runs parallel to the ground. If you were to plot various points along this line, like \((-5, 4)\) or \((0, 4)\), you'd see they all share the same y-value, confirming that this is indeed a line with a slope of 0.
