PARALLEL LINES IN THE COORDINATE PLANE

About "Parallel lines in the coordinate plane"

Parallel lines in the coordinate plane :

Parallel lines are two lines that never intersect. In the coordinate plane, that would look like this :

If we take a closer look at these two lines, the slope of both the lines is 1/2.

This can be generalized to any pair of parallel lines. Parallel lines always have the same slope and different yintercepts.

Postulate (Slopes of parallel lines) :

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

Slope of a line in coordinate plane

The slope of a non vertical line is the ratio of the vertical change (the rise) to the horizontal change (the run).

If the line passes through the points (x1, y1) and (x2, y2), then the slope is given by

Slope  =  rise / run

Slope  =  (y2 - y1 / (x2 - x1)

Usually, slope is represented by the variable m.

Parallel lines in the coordinate plane - Examples

Example 1 :

In the diagram given below, find the slope of each line. Determine whether the lines j1 and j2 are parallel.

Solution :

Line j1 has a slope of

m2  =  4/2  =  2

Line j2 has a slope of

m2  =  2/1  =  2

Since the slope of the lines jand jare equal, the lines jand jare parallel.

Example 2 :

In the diagram given below, find the slope of each line. Which lines are parallel ?

Solution :

Part 1 :

Find the slope of the line k1. Line k1 is passing through the points (0, 6) and (2, 0).

Let (x1, y1) =  (0, 6) and (x2, y2)  =  (2, 0)

Slope (k1)  =  (y2 - y1)  / (x2 - x1)

Slope (k1)  =  (0 - 6)  / (2 - 0)

Slope (k1)  =  - 6 / 2

Slope (k1)  =  - 3

Part 2 :

Find the slope of the line k2. Line k2 is passing through the points (-2, 6) and (0, 1).

Let (x1, y1)  =  (-2, 6) and (x2, y2)  =  (0, 1)

Slope (k2)  =  (y2 - y1)  / (x2 - x1)

Slope (k2)  =  (1 - 6)  / [0 -(-2)]

Slope (k2)  =  (1 - 6)  / [0 + 2]

Slope (k2)  =  - 5/2

Part 3 :

Find the slope of the line k3. Line k3 is passing through the points (-6, 5) and (-4, 0).

Let (x1, y1)  =  (-6, 5) and (x2, y2)  =  (-4, 0)

Slope (k3)  =  (y2 - y1)  / (x2 - x1)

Slope (k3)  =  (0 - 5)  / [-4 - (-6)]

Slope (k3)  =  - 5 / (-4 + 6)

Slope (k3)  =  - 5 / 2

Compare the slopes. Because k2 and k3 have the same slope, they are parallel. Line k1 has a different slope, so it is not parallel to either of the lines.

Example 3 :

Write an equation of the line through the point (2, 3) that has a slope 5

Solution :

Slope-intercept form equation of a line :

y  =  mx + b ------(1)

Substitute (x, y)  =  (2, 3) amd m  =  5

3  =  5(2) + b

Simplify

3  =  10 + b

Subtract 3 from both sides

-7  =  b

The equation of the required line is

(1) ------> y  =  5x - 7

Example 4 :

In the diagram given below,

Line n1 has the equation y  =  -x/3 -1.

Line n2 is parallel to the line n1 and passes through the point (3, 2).

Write the equation of the line n2.

Solution :

The slope of the line n1 is -1/3. Because the lines n1 and n2 are parallel, they have the same slope. So, the slope of the line n2 is also -1/3.

Slope-intercept form equation of a line :

y  =  mx + b ------(1)

Because the line n2 is passing through (3, 2), substitute aa(x, y)  =  (3, 2) amd m  =  -1/3

2  =  (-1/3)(3) + b

Simplify

2  =  -1 + b

3  =  b

The equation of the required line is

(1) ------> y  =  (-1/3)x + 3

y  =  -x/3 + 3

After having gone through the stuff given above, we hope that the students would have understood "Parallel lines in the coordinate plane".

Apart from the stuff given on "Parallel lines in the coordinate plane", if you need any other stuff in math, please use our google custom search here.

WORD PROBLEMS

HCF and LCM  word problems

Word problems on simple equations

Word problems on linear equations

Algebra word problems

Word problems on trains

Area and perimeter word problems

Word problems on direct variation and inverse variation

Word problems on unit price

Word problems on unit rate

Word problems on comparing rates

Converting customary units word problems

Converting metric units word problems

Word problems on simple interest

Word problems on compound interest

Word problems on types of angles

Complementary and supplementary angles word problems

Double facts word problems

Trigonometry word problems

Percentage word problems

Profit and loss word problems

Markup and markdown word problems

Decimal word problems

Word problems on fractions

Word problems on mixed fractrions

One step equation word problems

Linear inequalities word problems

Ratio and proportion word problems

Time and work word problems

Word problems on sets and venn diagrams

Word problems on ages

Pythagorean theorem word problems

Percent of a number word problems

Word problems on constant speed

Word problems on average speed

Word problems on sum of the angles of a triangle is 180 degree

OTHER TOPICS

Profit and loss shortcuts

Percentage shortcuts

Times table shortcuts

Time, speed and distance shortcuts

Ratio and proportion shortcuts

Domain and range of rational functions

Domain and range of rational functions with holes

Graphing rational functions

Graphing rational functions with holes

Converting repeating decimals in to fractions

Decimal representation of rational numbers

Finding square root using long division

L.C.M method to solve time and work problems

Translating the word problems in to algebraic expressions

Remainder when 2 power 256 is divided by 17

Remainder when 17 power 23 is divided by 16

Sum of all three digit numbers divisible by 6

Sum of all three digit numbers divisible by 7

Sum of all three digit numbers divisible by 8

Sum of all three digit numbers formed using 1, 3, 4

Sum of all three four digit numbers formed with non zero digits

Sum of all three four digit numbers formed using 0, 1, 2, 3

Sum of all three four digit numbers formed using 1, 2, 5, 6