Write an equation of the line passing through the point (-1, 1) and parallel to the given line y = -2.
Understand the Problem
The question is asking for the equation of a line that passes through a specific point and is parallel to another given line. The required equation needs to reflect the properties of parallel lines in geometry.
Answer
$y = 1$
Answer for screen readers
The equation of the line is $y = 1$.
Steps to Solve
- Identify the slope of the given line
The equation of the line is given as $y = -2$. This is a horizontal line where the slope ($m$) is $0$.
- Use the slope for the new line
Since the new line must be parallel to the given line, it will have the same slope, which is $0$. This means the new line is also horizontal.
- Write the equation of the new line
A horizontal line passing through the point $(-1, 1)$ will have the equation $y = 1$, since it maintains the same $y$-coordinate across all $x$.
The equation of the line is $y = 1$.
More Information
Parallel lines have the same slope. Hence, a line parallel to a horizontal line will also be horizontal, which is characterized by a constant $y$-value.
Tips
- Confusing the types of lines: Some may mistakenly try to find a slope or intercept when the problem involves a horizontal line. Remember that the slope of a horizontal line is always $0$.
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