Need Help?

Get in touch with us

bannerAd

Slopes of Lines

Sep 12, 2022
link

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. 

Slope of a line 

If a line in the coordinate plane passes through points (x1,y1) and (x2,y2)

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

parallel

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

SLOPE
SLOPE
SLOPE
SLOPE

Slopes of parallel lines 

In a coordinate plane, two non-vertical lines are parallel if and only if they have the same slope. 

parallel
Slopes of parallel lines 

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

Slopes of perpendicular lines 

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

Concept Map: 
Concept Map: 
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.

Comments:

Related topics

Composite Figures – Area and Volume

A composite figure is made up of simple geometric shapes. It is a 2-dimensional figure of basic two-dimensional shapes such as squares, triangles, rectangles, circles, etc. There are various shapes whose areas are different from one another. Everything has an area they occupy, from the laptop to your book. To understand the dynamics of composite […]

Read More >>
special right triangles_01

Special Right Triangles: Types, Formulas, with Solved Examples.

Learn all about special right triangles- their types, formulas, and examples explained in detail for a better understanding. What are the shortcut ratios for the side lengths of special right triangles 30 60 90 and 45 45 90? How are these ratios related to the Pythagorean theorem?  Right Angle Triangles A triangle with a ninety-degree […]

Read More >>
simplify algebraic expressions

Ways to Simplify Algebraic Expressions

Simplify algebraic expressions in Mathematics is a collection of various numeric expressions that multiple philosophers and historians have brought down. Talking of algebra, this branch of mathematics deals with the oldest concepts of mathematical sciences, geometry, and number theory. It is one of the earliest branches in the history of mathematics. The study of mathematical […]

Read More >>
solve right triangles

How to Solve Right Triangles?

In this article, we’ll learn about how to Solve Right Triangles. But first, learn about the Triangles.  Triangles are made up of three line segments. These three segments meet to form three angles. The lengths of the sides and sizes of the angles are related to one another. If you know the size (length) of […]

Read More >>

Other topics