Find the equation of the line that passes through (-5, -1) and is parallel to the line 3.
Understand the Problem
The question is asking for the equation of a line that passes through the point (-5, -1) and is parallel to another given line, which is implied to have a specific slope. To solve it, we will need to determine the slope of the line the new line is parallel to, and then use the point-slope form of the equation of a line.
Answer
The equation of the line is $y = -1$.
Answer for screen readers
The equation of the line is:
$$ y = -1 $$
Steps to Solve
- Identify the slope of the given line
The line described as "line 3" seems to have no specific slope mentioned. For horizontal lines, the slope is $0$. For vertical lines, it would be undefined. Assuming line 3 is horizontal, the slope will be:
$$ m = 0 $$
- Use the point-slope form of the equation of a line
The point-slope form of a line's equation is given by:
$$ y - y_1 = m(x - x_1) $$
Here, we know that the point the line passes through is $(-5, -1)$, which means $x_1 = -5$ and $y_1 = -1$. Since the slope $m = 0$, we can substitute these values into the equation:
$$ y - (-1) = 0(x - (-5)) $$
- Simplify the equation
Now simplify the equation:
$$ y + 1 = 0 $$
Since $0(x - (-5))$ is $0$, we simplify to find:
$$ y = -1 $$
This represents a horizontal line at $y = -1$.
The equation of the line is:
$$ y = -1 $$
More Information
This line is horizontal and passes through the point $(-5, -1)$. It maintains the same $y$-coordinate for all $x$ values because it's parallel to a horizontal line.
Tips
A common mistake is assuming the slope of the parallel line without checking its characteristics. Always confirm the slope of the given line before proceeding.
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