The line passes through (1,-2) and (-2,-2)
Understand the Problem
The question is asking for the equation or properties of a line that passes through the points (1, -2) and (-2, -2). To solve this, we can use the two points to determine the slope and then use the point-slope form of a line to get the equation.
Answer
The equation of the line is $y = -2$.
Answer for screen readers
The equation of the line is $y = -2$.
Steps to Solve
- Calculate the Slope of the Line
To find the slope ($m$) of the line passing through the points $(1, -2)$ and $(-2, -2)$, we can use the formula:
$$ m = \frac{y_2 - y_1}{x_2 - x_1} $$
Here, $(x_1, y_1) = (1, -2)$ and $(x_2, y_2) = (-2, -2)$.
Substituting the values:
$$ m = \frac{-2 - (-2)}{-2 - 1} = \frac{0}{-3} = 0 $$
- Identify the Type of the Line
Since the slope $m = 0$, this indicates that the line is horizontal. Horizontal lines have the same $y$-value for all points along the line.
- Write the Equation of the Line
For a horizontal line that passes through the point $(1, -2)$, the equation can simply be stated as:
$$ y = -2 $$
This means for any $x$ value, $y$ will always be $-2$.
The equation of the line is $y = -2$.
More Information
This means that no matter the value of $x$, the $y$ value will always remain $-2$. You can visualize this as a straight line running parallel to the x-axis at the height of $-2$.
Tips
- Confusing horizontal lines with vertical lines: Remember that horizontal lines have a slope of $0$ and vertical lines have an undefined slope.
- Forgetting to check if the $y$ values of both points are the same, which indicates a horizontal line.
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