Original subtitles

professor Dave again let's look at some

more lines we know how to graph lines in

a few different forms so let's start

comparing different types of lines to

see what we can learn from this first

let's take a look at a graph containing

two parallel lines these are lines in

the same plane that never intersect in

order for this to be the case the lines

must have the same ratio of vertical

change to horizontal change in other

words they must have equivalent slopes

their equations will be different

but their slopes are identical on the

other hand two lines that intersect at a

right angle are perpendicular to one

another the relationship between the

slopes of perpendicular lines is not as

obvious as it was for parallel lines but

as it turns out perpendicular lines have

slopes that are opposite reciprocals of

one another by opposite reciprocal we

mean that if one has a slope of 2 the

other has a slope of negative 1/2 if one

has a slope of negative 5 the other has

a slope of 1/5 we flip the term and flip

the sign there are many questions you

may encounter in algebra that require

you to understand these concepts for

example a question may ask you to write

the equation of any line that is

perpendicular to y equals negative 1/4 X

plus 2 if you are unaware of the

relationship between the slopes of

perpendicular lines you might find

yourself graphing this line and then

choosing an arbitrary perpendicular line

so you can find its equation but instead

of all this we just recognize that the

opposite reciprocal of this slope would

be positive 4 so any line with a slope

of 4 will satisfy the requirements y

equals 4x plus 6 or 4x minus a thousand

it doesn't matter if it has a slope of 4

it will intersect this line at a

angle somewhere some questions will

require that you be a little more

specific you could be asked to find the

equation of a line that is parallel to y

equals 3x plus 1 and goes through the

point 4 4 well if it's parallel we know

it has a slope of 3 so y equals 3x plus

B now we can plug in the coordinates for

the one point we know so 4 equals 3

times 4 plus B and if we solve for B we

get negative 8 so the equation must be y

equals 3x minus 8 we could do the same

thing for perpendicular lines say we

need to find the equation for the line

that is perpendicular to y equals 1/4 X

minus 2 and passes through the point

negative 2 9 well once again we know we

need the opposite reciprocal of the

slope that means 1/4 becomes negative 4

y equals negative 4x plus B we plug in

the coordinates of the point we have and

9 will equal negative 4 times negative 2

plus B this product is 8 we subtract 8

from both sides and B equals 1 so the

equation is y equals negative 4x plus 1

none of this is too tricky but it's

important to know these rules as these

are extremely common types of questions

in algebra so let's check comprehension

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as always feel free to email me

professor Dave explains at gmail.com

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