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### Course: Algebra 1>Unit 5

Lesson 5: Standard form

# 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?

• good one
(1 vote)
• 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.
• 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.
• 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'!
• 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)
• Why not just ust the 2 intercepts to find 2 pionts on the line?
• 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.
• 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.