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### Course: Algebra 1 > Unit 5

Lesson 5: Standard form- Intro to linear equation standard form
- Graphing a linear equation: 5x+2y=20
- Clarifying standard form rules
- Graph from linear standard form
- Converting from slope-intercept to standard form
- Convert linear equations to standard form
- Standard form review

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# Graphing a linear equation: 5x+2y=20

We can graph a the linear equation like 5x + 2y = 20 by rewriting it so y is isolated, then plugging in x values to find their corresponding y-values in a table. We can then graph those x-y pairs as points on a graph. Created by Sal Khan and Monterey Institute for Technology and Education.

## Want to join the conversation?

- Dear Algebra, Please stop asking us to find your X. She's never coming back, and don't ask Y.(42 votes)
- Hold on, can't you just turn the Standard form equation into a Slope Intercept form equation and then you would find the y-intercept, with the y-intercept can't you just count the slope using Rise/Run(Rise over Run)?(9 votes)
- Yes, that is an option for graphing a linear equation. Usually teachers like you to know that there are more than one way to graph a linear equation. Creating a table of values is an approach that works for all types of equations. Using the slope and y-intercept only works for linear equations.(8 votes)

- Isn't this just converting standard form into slope intercept form?(4 votes)
- The 1st part yes. But Sal also shows you how to calculate points on the line and draw the line.(11 votes)

- At2:30I dont understand how you cancel the 2 in the denominator with the 2 in the numerator(5 votes)
- If you have a fraction with only multiplication in the denominator and numerator (no addition or subtraction) you can cancel anything out if you have two identical numbers in the denominator and numerator, example

because 4 and 5 is in both the denominator and numerator.`(2 * 4 * 5) / (5 * 3 * 4) = (2) / (3)`

Mathematically we can explain it like this: You have the equation

We can rewrite`y = 10 - (5 * 2)/2`

Here you can see that`(5 * 2)/2 = 5 * (2/2)`

So`2/2 = 1`

Your equation can be rewritten as`(5 * 2)/2 = 5 * 1 = 5`

`y = 10 - (5 * 2)/2 = 10 - 5 * (2/2) = 10 - 5 * 1 = 10 - 5`

(6 votes)

- when you're looking for y, does your x HAVE to go by 2's?(4 votes)
- In this equation no.

He is just going by "2's" because that's what 'x' represents.

In reality When x = 2 then y = 10 - 5/2 *2

So he is just SOLVING for '2' you could incert a differbt number other than '2'!(8 votes)

- yes, you have to use it for most, if not all equations/expressions/problems (and in response to the comment above, PEMDAS is order of operations, i.e. parentheses, exponents, multiplication, division, addition, and subtraction)(10 votes)

- Why not just ust the 2 intercepts to find 2 pionts on the line?(4 votes)
- Yes, you can do that. But be aware, you need a minimum of 2 points and some lines will only give you one point if you go for the intercepts. For example:

-- For some lines, the X and Y intercepts are the origin (0,0). So one point is both intercepts.

-- Horizontal lines only have a y-intercept

-- Vertical lines only have an x-intercept

So, you need to understand the basic concepts of how to find other points for the lines besides the intercepts.

There is also value in finding 3 points rather than 2 point to graph your line. The 3rd point acts as your quality check. If you can calculate 3 points that fall on the same line, you have a low risk of having made math error. If the 3 points are not lining up, then you know at least 1 point has a calcuation or graphing error.

Hope this helps.(5 votes)

- how do you do this when your y= 5/2 - 1x then what would you do to you with the fraction would you simplify or leave it as 5/2 ?(3 votes)
- As long as the value stays the same you can leave it as whatever is easier for you, or whatever you're told to do with it.

For me I like it like this, because you can specifically see the slope as rise over run, where it rises 5 and runs 2.(5 votes)

- Wouldn't it be quicker if we make use of the fact this is in standard form to plot and link the X and Y intercepts instead of picking two arbitrary points tho?(2 votes)
- To be honest, yes, since we can deduce the x-intercept and y-intercept immediately.

ax + by = c

x-intercept: c / a

y-intercept: c / b

No idea why they even taught standard form in the first place if we're changing it to slope-intercept form anyway lol(6 votes)

- Why is algebra so difficult and complex for no reason T~T(2 votes)
- Don't worry; algebra is one of those subjects that is super hard to wrap one's brain around. While it may seem difficult, everything will fall into place with practice.(6 votes)

## Video transcript

Create a graph of the
linear equation 5x plus 2y is equal to 20. So the line is
essentially the set of all coordinate,
all x's and y's, that satisfy this relationship
right over here. To make things simpler,
what we're going to do is set up a table
where we're going to put a bunch of x values
in and then figure out the corresponding y value
based on this relationship. But to make it a
little bit simpler, I'm going to solve for y here. So it becomes easier to
solve for y for any given x. So we have 5x plus
2y is equal to 20. If we want to solve
for y, let's just get rid of the 5x on
the left-hand side. So let's subtract 5x from
both sides of this equation. The left-hand side,
these guys cancel out, so we get 2y is equal
to the right hand side, you have 20 minus 5x. And then you can divide both
sides of this equation by 2. So you divide both sides by 2. The left-hand side, we
just have a y, and then the right-hand side, we
could leave it that way. That actually would be a
pretty straightforward way to leave it, or we could
call this 20 divided by 2 is 10 minus 5x over 2
or minus 5/2 times x. And so now using
this, let's just come up with a bunch
of x values and see what the corresponding y values
are, and then just plot them. So let me do this
in a new color. So let me-- a slightly
different shade of yellow. So we have x values,
and then let's think about what
the corresponding y value is going to be. So I'll start, well, I
could start anywhere. I'll start at x is equal
to 0, just because that tends to keep things
pretty simple. If x is 0, then y is equal
to 10 minus 5/2 times 0, which is equal to
5/2 times 0 is just a 0. So it's just 10 minus 0 or 10. So that gives us the coordinate,
the point, 0 comma 10. When x is 0, y is 10. So x is 0. So it's going to be right here
at the middle of the x-axis. And you go up 10 for
the y-coordinate. 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. So it's right over here. So that's the point 0 comma 10. Let's do another point. Let's say that x is 2. I'm going to pick
multiples of 2 here just so that I get a
nice clean answer here. So when x is 2, then y is
equal to 10 minus 5/2 times 2, and the 2 in the
denominator cancels out with this 2 in the numerator. So it simplifies to
10 minus 5, or just 5. So that tells us the point
x equals 2, y is equal to 5, is on the line. So 2x is equal to 1,
2 right over here. And then y is equal to 5. You go up 5. 1, 2, 3, 4, 5, just like that. So that's the point 2, 5. And when you're drawing
a line you actually just need two points. If you have a ruler or
any kind of straight edge, we could just connect
these two points. And if we do it neatly,
every point on that line should satisfy this
relationship right here. Just so we get practice,
I'll do more points. So let me do, let's say
when x is equal to 4, then y is equal to
10 minus 5/2 times 4. This is equal to 5/2 times 4. This is equal to 10, right? Because the 2, divide the
denominator by 2 you get 1, divide the numerator by
2 you get 2, or 4 over 2 is the same thing as 2. So it becomes 2 times 5
is 10, 10 minus 10 is 0. So the point 4 comma
0 is on our line. So x is 1, 2, 3,
4, and then y is 0. So we don't move up at
all, so we have 4 comma 0. And I could keep going. I could try other points. You could do them if you
like, but this is plenty. Just two of these would have
been enough to draw the line. So let me just draw it. So I'll do it in white. So the line will look
something like this. And I could keep going
in both directions. So there you have it. That is the graph of
our linear equation. Let me make my line
a little bit bolder, just in case you found that
first line hard to read. So let me make it a
little bit bolder. And I think you get
the general idea.