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## Algebra 1

### Course: Algebra 1>Unit 5

Lesson 5: Standard form

# Intro to linear equation standard form

The standard form for linear equations in two variables is Ax+By=C. For example, 2x+3y=5 is a linear equation in standard form. When an equation is given in this form, it's pretty easy to find both intercepts (x and y). This form is also very useful when solving systems of two linear equations.

## Want to join the conversation?

• I thought that in slope interecept form, the m&b can't be less than zero... so how are those numbers negative?
• There is nothing in slope-intercept form about m or b needing to be positive. In fact they are quite often negative or 0.
• What do "x" and "y" represent? For example, M is the slope, and B is the y-intercept.
• Just to be a little more precise, x and y are variables that take real values (like 1/2, -6, 0, etc.). A "line" is just a shape that corresponds to a special relationship between x and y. In particular, a line is the set of points that follow a certain rule (that rule looks like y=mx+b or y-y1=m(x-x1) or ax=by=c, etc.). All those equations are describing a relationship between two variables and when plotted, happen to take the shape of a straight line!
Given the equation of a line, we can immediately find the slope and y-intercept (assuming they're not undefined like in the case of a vertical line). There's not just one (x,y) corresponding to a line (that would just be a point!) so we let x and y vary to show the relationship those two variables have at a bunch of different values of x and y. Hope that helps and didn't confuse anyone more!
• Me: This is to difficult. Sal: Hold my cup.
• What does C stand for? y intercept?
• I know this is a 4 year old question, but I would like to answer for the sake of others wanting to know the answer as well.

So when you convert the y-intercept(y=1/2x+10) equation to Standard form you have to get the y-intercept by itself, subtract 1/2x from both sides BUT, the A value (slope) is a positive INTEGER.
-1/2x+y= 10 will become x-2y=-20.

Hope you understand, and if you have a question, then feel free to ask... and remember, Math Is Unbreakable.
• At ,

I love how Sal makes a mistake.
And my question is: am I the only only who loves Sal making a mistake?
• You're the evil student we've all been waiting for.
• At , why is 8 becoming a negative? Why isn't 4.5 a negative?
• The reason 4.5 isn't a negative is because Sal had said " From 8 to 0 we would have to change x (8) to -8. So 8 - 8 = 0. Simple. Same for 0 to 4.5. 0 + 4.5 = 4.5.

Hoped this helped, I am also trying to learn this by myself for the first time, so all the details might not be crystal clear for me and for you too.
• Isn't it easy to figure out the slope in standard form by using the coefficients of the y and x terms? Like dividing -9 by 16 in the example Sal uses.
• I found it illuminating to look at it from that angle, in conjunction with conversion to slope-intercept form.
• How would you go from standard form to point-slope form?
• Good question. It's actually hard (and not necessary in most cases) to go from standard form to point-slope form, because there is an infinite number of point-slope form equations for a linear function.
First solve for y and turn the equation into slope-intercept form.(this is for the slope)
Next, plug in a random number in for x-value as long as the x-value is in the domain of the function, and solve for y.(this is for a point that satisfies the equation)
Now you have the slope and a point, write the equation in point-slope form. You will get a different point-slope form for each point you choose.
• can anybody help me figure out how to find out whether an equation is linear?
• An equation is linear if there is a common difference (the change is either adding or subtracting by the same number each time)

You can also tell based on the equation:
y=mx+b
f(x)=mx+b

Hope that helps!