A line segment has endpoints D (3, 2) and E (-3, -2). The point F is the midpoint of DE. What is an equation of a line parallel to DE and passing through F?

Since F lies on DE, all we need is the equation of DE

We don't even need F

slope DE = (-2-2)/(-3-3) = 2/3
so y = (2/3)x + b
but (3,2) lies on it, so
2 = (2/3)(3) + b
b = 0

y = (2/3) x is the equation

check:
F is the origin (0,0) which satisfies y = (2/3)x

A rather strangely worded question.

To find the equation of a line parallel to DE and passing through F, we need to determine the slope of the line DE. The slope of a line passing through two points (x1, y1) and (x2, y2) is given by the formula:

m = (y2 - y1) / (x2 - x1)

Let's calculate the slope m for DE using the coordinates of the endpoints D and E:

m = (-2 - 2) / (-3 - 3)
= (-4) / (-6)
= 2/3

Now that we have the slope of DE, we can use it to find the equation of a line parallel to DE. A line parallel to DE will have the same slope (2/3).

The equation of a line in slope-intercept form (y = mx + b) is characterized by its slope (m) and y-intercept (b). We already know the slope (2/3), but we need to find the y-intercept (b).

Since F is the midpoint of DE, we can use its coordinates (x, y) = (0, 0) to determine the y-intercept. Substituting these values into the slope-intercept equation, we get:

0 = (2/3)(0) + b

Simplifying, we find:

0 = b

Therefore, the y-intercept (b) is 0.

Now we have the slope (2/3) and the y-intercept (0), which allows us to write the equation of the line parallel to DE and passing through F:

y = (2/3)x + 0
y = (2/3)x

So, the equation of a line parallel to DE and passing through F is y = (2/3)x.