Slopes of Lines
Key Concepts
- Define slope of a line
- Find the slopes of lines in the coordinate planes
- Compare slopes of lines
- Identify parallel lines and perpendicular lines using their slopes
Slope of a line
The ratio of vertical change (rise) to horizontal change (run) between any two points on the line is the slope of the line.
If a line in the coordinate plane passes through points (x1,y1) and (x2,y2)
Then the slope of the line is
m=change in y /change in x
=y2−y1 / x2−x1
Slopes of the lines in a coordinate plane
If a line rises from left to right, it is said to have a positive slope.
A horizontal line has zero slope (slope of 0).
When a line falls from left to right, it is said to have a negative slope
A vertical line has an undefined slope.
Slopes of parallel lines
In a coordinate plane, two non-vertical lines are parallel if and only if they have the same slope.
Slopes of perpendicular lines
In a coordinate plane, two non-vertical lines are perpendicular if and only if the product of their slopes is −1
.
Exercise
- Line n passes through (0,2) and (6,5). Line m passes through (2,4) and (4,0). Is n⊥m? Explain.
- Line q passes through (0,0) and (-4,5). Line t passes through (0,0) and (-10,7). Which line is steeper, q or t?
- Find the slope of the line that passes through the points (-5,-1) and (3,-1).
- Graph the line through the given point with the given slope.
- P(-4,0) and slope 5/2
- Graph a line with the given description.
- Through (1,3) and perpendicular to the line through (-1,-1) and (2,0).
Concept Map
What we have learned
- The ratio of vertical change (rise) to horizontal change (run) between any two points on the line is the slope of the line.
- The slopes of parallel lines are equal.
- The product of slopes of perpendicular lines is -1.
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