In this episode of Engineer In Training Exam TV, Justin walks you through a Fundamentals of Engineering Exam Review of Lines.

He will start with defining the rules of linear equations, then move on to discussing the different forms of a linear equation, and finish off with a quick example of a potential line problem on the exam.

This Fundamentals of Engineering Exam Review of Lines is part of the global subject Mathematics.

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Hey what’s going on everyone, it’s Justin Dickmeyer from EngineerInTrainingExam.com.

In today’s video we are going to present a Fundamentals of Engineering Exam Review of Lines.

We’ll start off this tutorial discussing the theory and then get in to working a problem.

So let’s start off our Fundamentals of Engineering Exam Review of Lines by defining exactly what a line is.

we call linear equation in two

variables is the equation y is equal to

5x plus 1 the two variables are

typically x and y but don’t necessarily

always have to be x and y in linear

equations linear equation or lines also

adhere to four rules number one the

variables x and y are raised to the

first only to the first power so the

variables x and y are to the first power

the second rule is that the variables

may be multiplied only by real numbers

so the variables

can be multiplied by only real numbers

the third rule is that any real number

term may be added or subtracted so any

real number term can be added or

subtracted and finally number four

nothing else is permitted nothing else

is permitted so that is to say that if

you’re given an equation and you see

that that equation has x squared if it

has y squared if has 1 over X east to

the X whatever anything not to the first

power then it is not a linear equation

so if you see look back at our example

here our general example this is an

equation where x and y is both to the

first power the variables are multiplied

by real numbers and there’s a real

number that is added in this case so

this equation adheres to all four rules

and we can call it a linear equation or

a line so what do we need to define a

line well we need two distinct pieces of

information concerning that line to

define it so in other words number one

if we are given two points for given two

points X x1 and y1 and x2 and y2 then we

can define the equation to that line or

if we are given one point

say x1 and y1 and the slope of the line

then we can also define the equation of

that given line a line can be

Illustrated using three different forms

the first one is the standard form or

also known as the point intercept form

and this is the one that we are most

used to seeing probably and that is y is

equal to MX plus B so in this case we’re

given the slope and we’re probably given

the intercept and we can just go ahead

and define that line simple the second

is the point-slope form and so say we’re

given the points x1 and y1 and we’re

also given the slope then we can go

ahead and write it in the point-slope

form which is y minus y1 is equal to M X

minus x1 so as you can see we have if

we’re given a point and the slope we

have the point here we just plug in our

information and we have the slope right

there the third form is called the

two-point form so say we’re given x1 y1

and we’re given x2 y2 if we’re given two

points then we can go ahead and plug

these points into the equation y minus

y1 is equal to y2 minus y1 divided by x2

minus x1 multiplied by X minus x1 so

these are the three forms of a straight

line or linear equation so let’s look at

a quick example here let’s say that we

have a problem and we’re given two pole

let’s say that those points are negative

2 1 & 1 2 let’s say that we want to find

or define this line given the two-point

form we know that the two-point form

equation is y minus y1 is equal to y2

minus y1 divided by x2 minus x1

multiplied by X minus x1 so all we need

to do is since we have both x1 and y1

and x2 and y2 all we need to do is plug

that information simply into the

equation we get y -1 is equal to Y 2 is

2 y 1 is 1 divided by X 2 1 minus

negative 2 multiplied by X minus x1

which isn’t so what we get is as we play

this out we get Y minus 1 is equal to 1

over 1 plus 2 which is 1 3 multiplied by

X plus 2 multiplying that through we got

1/3 X plus 2/3 and +1 adding one to each

side to get Y by itself

now just combine all the terms and we

got Y is equal to 1/3 X plus 5/3

so we use the point or the two-point

form here to define the equation and we

actually put that equation into the

standard form

so that’s it a pretty straightforward

tutorial just wanted to review real

quick

lines so if you guys have any more

questions or want to see any future

tutorials go ahead and visit engineer

and training exam com

check out the videos that I got up there

or contact me via the contact ask any

questions or get any free study

resources study guidance or whatnot so

look forward to talking to you guys soon

you guys take care alright bye

—

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