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.