Question

line a passes through the points (6, 1) and (-4, 6). line b passes through the points (14, 3) and (-10, -9). which statement is true? line a intersects line b at exactly one point. line a overlaps line b. line a does not intersect line b.

Explanation:

Step1: Calculate slope of Line A

The slope formula is $m = \frac{y_2 - y_1}{x_2 - x_1}$. For Line A with points $(6, 1)$ and $(-4, 6)$:
$m_A = \frac{6 - 1}{-4 - 6} = \frac{5}{-10} = -\frac{1}{2}$

Step2: Calculate slope of Line B

For Line B with points $(14, 3)$ and $(-10, -9)$:
$m_B = \frac{-9 - 3}{-10 - 14} = \frac{-12}{-24} = \frac{1}{2}$

Step3: Analyze slopes

Since $m_A = -\frac{1}{2}$ and $m_B = \frac{1}{2}$, the slopes are not equal (so lines are not parallel or overlapping) and not negative reciprocals (so not perpendicular). Non - parallel lines in a plane intersect at exactly one point.

Answer:

Line A intersects line B at exactly one point.