Find the slope of XY. X(0, a), Y(-a, 2a)
Understand the Problem
The question is asking to find the slope of the line segment XY given the coordinates of points X and Y. To find the slope, we will use the formula for slope, which is (y2 - y1) / (x2 - x1).
Answer
The slope of the line segment XY is $-1$.
Answer for screen readers
The slope of the line segment XY is $-1$.
Steps to Solve
- Identify the coordinates of points X and Y
The coordinates are given as follows:
- Point X: $X(0, a)$
- Point Y: $Y(-a, 2a)$
- Apply the slope formula
The slope $m$ of the line segment connecting points X and Y is calculated using the formula:
$$ m = \frac{y_2 - y_1}{x_2 - x_1} $$
Here, let:
- $x_1 = 0$, $y_1 = a$ (for point X)
- $x_2 = -a$, $y_2 = 2a$ (for point Y)
Substituting the values into the formula, we get:
$$ m = \frac{2a - a}{-a - 0} $$
- Simplify the expression
Calculating the numerator:
$$ 2a - a = a $$
And the denominator is:
$$ -a - 0 = -a $$
Now substitute back into the slope formula:
$$ m = \frac{a}{-a} $$
- Final calculation of the slope
Now simplify the fraction:
$$ m = -1 $$
The slope of the line segment XY is $-1$.
More Information
The slope of a line indicates its steepness and direction. A slope of $-1$ means that for every unit you move horizontally to the left, you move down one unit vertically, resulting in a diagonal line downwards from left to right.
Tips
- Incorrectly identifying coordinates: Make sure to assign $(x_1, y_1)$ and $(x_2, y_2)$ accurately.
- Sign errors: Be careful with the negatives, especially in the denominator.
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