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### Course: Algebra 1>Unit 5

Lesson 6: Summary: Forms of two-variable linear equations

# Writing linear equations in all forms

Sal finds the equation of a line that passes through (-3,6) and (6,0) in point-slope, slope-intercept, and standard form. Created by Sal Khan and Monterey Institute for Technology and Education.

## Want to join the conversation?

• but how do you graph it. my algebra teacher wants me to graph it without putting it into slope intercept form.
• Well, say the equation is 8x -2y =24. To graph, you must plug in 0 for either x or y to get the y- or x-intercept. So in the equation that I said, let's find the y-intercept first. You would plug in 0 for x. So the equation would be 8*0 -2y =24, or -2y =24. Then you can solve it like a regular equation and you would get y =-12. For the x-intercept, it's basically the same thing, except you plug in 0 for y instead of x. So you would get 8x -2*0 =24 or 8x =24. Once again, you would solve it like a regular equation, and get x =3. So the y-intercept is -12 and the x-intercept is 3. Then you can use those two points [(3,0) and (0,-12)] to find the slope and graph from there. I know this is a little late and you've probably figured it out by now, but I'm still posting this for those out there who had the same question and have not figured it out.
• He says 'if you WANT to make it look extra clean' to get rid of the fraction, but isn't one of the rules of Standard Form that you can't have fractions? Wouldn't you have to get rid of that fraction anyway?
• You wouldnt have to. It would really just depend on how your professor would like the form to be.
• At ,Sal says that the equation is in standard form.I thought you couldn't have fractions in standard form.Can someone explain please?
• I'm not sure, but the way I learned it, you are right. it should be 2x+3y=12
• how would you know if the line is a parrallel line
y=2/3x-2
• well if slope of line 1 is equal to slope of line 2 they are parallel
lets say if equation of line 1 is y=m1x+c
and line 2 is y=m2x+c
then m1 and m2 should be equal in order to make them parallel
m1=m2
• In standard form, shouldn't A in Ax+By=C always be positive?
• Not necessarily.

A Linear equation in standard form is written as Ax + By = C, This does not mean that A should always be Positive. But by convention, the equation is written in a way that we get A >= 0.

• what is the point of the video😑😐😶🙄
(1 vote)
• Despite the fact that you just called me a "nerd" in a comment you posted on another entry, I'm going to try and answer you question anyway. Maybe it's time for you to find some of your own "inner nerd".

What is the point of the video? Linear equations can appear in different forms. Each form has it's own benefits. This video is showing you the different forms and how you can create the equation for a line given two points that are on the line.
• *Which is better to use and which is easier to use?*
• I think y=mx+b is the easiest formula. I think it is the easiest because you can easily graph it, also if you need to change it into the other formulas it can be done easily. But everyone has different opinions so find the best that works for you, good question.
• At , Sal says he will use the point (-3,6) for the point slope form. Does it matter what point you use for the point slope form? In some of the Khan Academy exercises, the questions say I am wrong when I use different points for point-slope form.
• It does not matter which point you use in point slope form. If your answer is marked wrong, then you much have an error. If you tried posting your problem and your work, then someone could help you find your error.
• At 4.33, Sal uses 6 as his b for the point slope mode: y - b = mx (x-a) -> y - 6 = -2/3(x--3).

But at 5.49 he uses mx * a to define his b for the slope intercept mode. And therefore his b ends up being 4 in the final slope intercept mode: y = mx + b -> y = -2/3x+4.

When y= mx+b, why is y = -2/3 + 6 not a valid answer? This was my natural instinct, when i tried to solve for the slope intercept mode before the point slope mode.