Question

Which best describes the relationship between the line that passes through the points (-9, 2) and (-5, 4) and the line that passes through the points (-3, 4) and (1, 6)?

a) Parallel lines
b) Perpendicular lines
c) Intersecting lines
d) Coinciding lines

Answer 1

Both lines have a slope of 0.5 and since they are the same, they are parallel lines. They will never cross each other.

Step-by-step explanation:

To determine the relationship between the two lines described by the given points, we must compare their slopes. The slope of a line that passes through two points (x1, y1) and (x2, y2) can be found using the formula (y2 - y1) / (x2 - x1). For the first line passing through points (-9, 2) and (-5, 4), the slope is (4 - 2) / (-5 + 9) which simplifies to 2 / 4 or 0.5. For the second line passing through points (-3, 4) and (1, 6), the slope is (6 - 4) / (1 + 3) which simplifies to 2 / 4 or 0.5 as well.

Since both lines have the same slope, they will never cross each other, indicating that they are parallel lines.