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## Class 9 (Old)

### Course: Class 9 (Old)>Unit 4

Lesson 2: Graph of a linear equation in two variables

# 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?

• ha ha ha
• 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)?
• 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.
• when you're looking for y, does your x HAVE to go by 2's?
• 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'!
• Isn't this just converting standard form into slope intercept form?
• The 1st part yes. But Sal also shows you how to calculate points on the line and draw the line.
• At I dont understand how you cancel the 2 in the denominator with the 2 in the numerator
• 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
``(2 * 4 * 5) / (5 * 3 * 4) = (2) / (3)``
because 4 and 5 is in both the denominator and numerator.

Mathematically we can explain it like this: You have the equation
``y = 10 - (5 * 2)/2``
We can rewrite
``(5 * 2)/2 = 5 * (2/2)``
Here you can see that
``2/2 = 1``
So
``(5 * 2)/2 = 5 * 1 = 5``
Your equation can be rewritten as
``y = 10 - (5 * 2)/2 = 10 - 5 * (2/2) = 10 - 5 * 1 = 10 - 5``
• do you use Pemdas on this?
• 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)
• 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 ?
• 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.
• At can we not simplify the linear equation?!
• It seems to me that he is doing it the easiest way. But if you think it's easier to introduce a fraction from the start, go ahead.
• my teacher gives my questions like y=5/3x - 2. How do I solve for y?
• In this case, it's impossible to find out the solution mathematically without guessing and checking. You should have another equation.
• what happens if you were to switch the x and y axis?
• This cant happen the graph can only work in one way.

## 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.