Given (-5, -2) and (-6, -8), find the slope.
Understand the Problem
The question is asking to calculate the slope between two points, (-5, -2) and (-6, -8). The slope can be determined using the formula (y2 - y1) / (x2 - x1).
Answer
The slope is $m = 6$.
Answer for screen readers
The slope between the points ((-5, -2)) and ((-6, -8)) is $m = 6$.
Steps to Solve
- Identify the points The two points given are ((-5, -2)) and ((-6, -8)). We can label them as:
- Point 1: ((x_1, y_1) = (-5, -2))
- Point 2: ((x_2, y_2) = (-6, -8))
- Apply the slope formula The formula for calculating the slope (m) between two points is:
$$ m = \frac{y_2 - y_1}{x_2 - x_1} $$
- Substitute the values Now, substitute the coordinates into the formula:
$$ m = \frac{-8 - (-2)}{-6 - (-5)} $$
- Simplify the numerator and denominator Calculate the numerator and denominator:
Numerator: $$ -8 - (-2) = -8 + 2 = -6 $$
Denominator: $$ -6 - (-5) = -6 + 5 = -1 $$
- Calculate the slope Now, plug the simplified values back into the slope equation:
$$ m = \frac{-6}{-1} = 6 $$
The slope between the points ((-5, -2)) and ((-6, -8)) is $m = 6$.
More Information
The slope represents the rate of change of (y) with respect to (x) between the two points. A positive slope indicates that as (x) increases, (y) also increases.
Tips
- Incorrectly Subtracting Coordinates: Make sure to pay attention to the signs when subtracting the (y) and (x) coordinates.
- Neglecting to Simplify: Failing to simplify the fractions after substitution can lead to incorrect answers.