To find the slope of line segment [tex]\(DC\)[/tex], we need to examine the relationship between the coordinates of points D and C.
1. Identify Coordinates:
Assume points [tex]\(D\)[/tex] and [tex]\(C\)[/tex] lie on the cartesian plane with coordinates [tex]\(D(x_1, y_1)\)[/tex] and [tex]\(C(x_2, y_2)\)[/tex], respectively.
2. Formula for Slope:
The formula for the slope [tex]\(m\)[/tex] of a line passing through two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] is given by:
[tex]\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\][/tex]
3. Given Slope:
We need to verify the slope of [tex]\(DC\)[/tex]. Given that the slope [tex]\(m\)[/tex] of [tex]\(DC\)[/tex] is [tex]\(-\frac{2}{5}\)[/tex], this means that:
[tex]\[
m = -\frac{2}{5}
\][/tex]
4. Interpretation of Slope:
The slope of [tex]\(-\frac{2}{5}\)[/tex] suggests that for every 5 units of horizontal change (in the [tex]\(x\)[/tex]-direction), the vertical change (in the [tex]\(y\)[/tex]-direction) is [tex]\(-2\)[/tex] units. This means that the line segment [tex]\(DC\)[/tex] is decreasing as you move from left to right.
Therefore, the slope of line segment [tex]\(DC\)[/tex] is [tex]\(-0.4\)[/tex].
