To determine the slope of the line passing through the points [tex]\((82, -96)\)[/tex] and [tex]\((87, -86)\)[/tex], we use the slope formula:
[tex]\[ \text{slope} = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]
Let's identify the coordinates from the points given:
- [tex]\((x_1, y_1) = (82, -96)\)[/tex]
- [tex]\((x_2, y_2) = (87, -86)\)[/tex]
Next, we calculate the difference in the [tex]\( y \)[/tex]-coordinates ([tex]\( y_2 - y_1 \)[/tex]):
[tex]\[ y_2 - y_1 = -86 - (-96) = -86 + 96 = 10 \][/tex]
Then, we calculate the difference in the [tex]\( x \)[/tex]-coordinates ([tex]\( x_2 - x_1 \)[/tex]):
[tex]\[ x_2 - x_1 = 87 - 82 = 5 \][/tex]
Now, we find the slope by dividing the difference in the [tex]\( y \)[/tex]-coordinates by the difference in the [tex]\( x \)[/tex]-coordinates:
[tex]\[ \text{slope} = \frac{10}{5} = 2.0 \][/tex]
Therefore, the slope of the line passing through the points [tex]\((82, -96)\)[/tex] and [tex]\((87, -86)\)[/tex] is [tex]\(2.0\)[/tex].
