Parallel and perpendicular lines in linear functions - Linear Functions

Parallel and perpendicular lines in linear functions

Parallel lines are lines with identical slope. In other words, these lines will never cross each other. Perpendicular lines will always pass through each other and form right angles at the interception. In this lesson, we will learn how to use information such as, points in lines and their slopes, to determine whether the lines are parallel, perpendicular or neither.

Related concepts:
Parallel line equation
Perpendicular line equation
Combination of both parallel and perpendicular line equations

Lessons

Notes:

Parallel
lines $-$ identical slope so they never intersect each other, unless overlapped.

Perpendicular
lines $-$ two lines form right angles to each other when they intersect. If the slope of first line is ${a \over b}$ , the slope of perpendicular line is the slope of perpendicular line is $- {b \over a}$ . The product of the two slopes is -1.

Intro Lesson
3.
Given the points of two lines, determine when the lines are parallel, perpendicular or neither.

Parallel and perpendicular lines in linear functions

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AlgebraSlope equation: m=y2−y1x2−x1m = \frac{y_2-y_1}{x_2- x_1}m=x2​−x1​y2​−y1​​

AlgebraSlope intercept form: y = mx + b

AlgebraPoint-slope form: y−y1=m(x−x1)y - y_1 = m (x - x_1)y−y1​=m(x−x1​)

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Slope equation: m=y2−y1x2−x1m = \frac{y_2-y_1}{x_2- x_1}m=x2​−x1​y2​−y1​​

Slope intercept form: y = mx + b

Point-slope form: y−y1=m(x−x1)y - y_1 = m (x - x_1)y−y1​=m(x−x1​)

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Lesson: 3a

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Lessons

Notes:

Intro Lesson

a)

Definition of Parallel and Perpendicular Lines How does that relate to slope?

1.

Determine whether the three points A (-2,-1), B(0,4) & C(2,9) all lie on the same line.

2.

3.

Given the points of two lines, determine when the lines are parallel, perpendicular or neither.

a)

Line 1: (3,2) & (1,4); Line 2: (-1,-2) & (-3,-4)

b)

Line 1: (5,6) & (7,8); Line 2: (-5,-6) & (-7,-8)

4.

Show that the points A(-3,0), B(1,2) and C(3,-2) are the vertices of a right triangle.

5.

Show that the points A(-1,-1), B(3,0), C(2,4) and D(-2,3) are the vertices of a square.

Parallel and perpendicular lines in linear functions

Don't just watch, practice makes perfect.

We have over 1850 practice questions in Algebra for you to master.

Algebra
Slope equation: $m = \frac{y_2-y_1}{x_2- x_1}$

Algebra
Slope intercept form: y = mx + b

Algebra
Point-slope form: $y - y_1 = m (x - x_1)$

Slope equation: $m = \frac{y_2-y_1}{x_2- x_1}$

Point-slope form: $y - y_1 = m (x - x_1)$

or

Definition of Parallel and Perpendicular Lines

How does that relate to slope?