Line Relationship
Consider one straight line passing through the points (0, 5) and (2,15), while another straight line passes through points (7, -4) and (9, 6). Are these lines parallel, perpendicular, or do they intersect at a non 90° angle?
Expand Hint
Given two points, the slope is:
$$$m=\frac{rise}{run}=\frac{y_2-y_1}{x_2-x_1}$$$
Hint 2
Slopes of perpendicular lines are the negative reciprocals of each other. Parallel lines have identical slopes.
The first step is to find the slope values for both lines. Given two points, the slope is:
$$$m=\frac{rise}{run}=\frac{y_2-y_1}{x_2-x_1}$$$
$$$m_1=\frac{15-5}{2-0}=\frac{10}{2}=5$$$
$$$m_2=\frac{6-(-4)}{9-7}=\frac{10}{2}=5$$$
Because
$$m_1$$
and
$$m_2$$
are identical, these two slopes are parallel. Perpendicular lines have negative reciprocal slopes, while non 90° intersections will have different slopes.
Parallel
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