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### Course: Integrated math 1>Unit 5

Lesson 1: Intro to slope-intercept form

# Intro to slope-intercept form

Slope-intercept form (y=mx+b) of linear equations highlights the slope (m) and the y-intercept (b) of a line. Watch this video to learn more about it and see some examples.

## Want to join the conversation?

• My teacher actually said something about "rise over run." Could you talk little bit more about it?
• rise/run is basically another term name for y/x because for the "y" axis it rises or goes up vertically and the "x" axis runs or goes across horizontaly.
• What is the difference between y=mx+c and y=mx+b?
• Nothing... They just use different variables for the y-intercept.
• I'm confused, by how did he got (y - 5) = 2 (x - 1) also can somebody reply quick because I'm just stuck right now
• I dont like this unit
• i agree
• i think my brain is broken i don't understand any of this
• Lets say, idk, y=3x+6. This is saying that when x is chilling at 0, then y is all the way at 6. And every time lazy x goes up 1, then y has to go up three.That is what he's saying with the whole equation. What he is doing is he's showing a graph of what is happening in that whole equation thingy. The chart helps us stay organized, and helps with all the points, because otherwise math people would get confused. Hope this helps. :)
• How many different way can you write an equation?
• Infinitely many. You can rewrite equations by performing algebraic manipulations, making sure you always do the same operation on both sides of the "=" sign. So you could add 1 to both sides, and now it's written a new way. Or add 2 to both sides, or add 9, or subtract 3.5, or multiply by 617.8, etc.
• Sometimes, I see slope intercept form written as "y=mx+a" instead of the typical y=mx+b. There are other variations of it like y=m(x-a). Could anyone articulate on this variation of slope intercept form?
• The forms y=mx+b and y=mx+a are essentially the same, except for the naming of the constant term. The form y=mx+b means slope m and y-intercept b; similarly, the form y=mx+a means slope m and y-intercept a.

The form y=m(x-a) is essentially different from the other two forms, and means slope m and x-intercept (instead of y-intercept) a.

Have a blessed, wonderful day!
• I read that y=m(x-a) is slope-intercept from, where m=slope and a=x-intercept. How do you derive that from the simpler slope-intercept form?
• As noted in your other post, rather than being derived from the slope intercept form, it is a variation of the point slope form, y - y1 = m(x-x1) where the point is (x1,y1) and the slope is m. Since the x intercept is where y = 0, the point would revert to (x1,0), thus reaching your form of y=m(x-x1), merely substituting a for x1 does not change the formula.