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## Algebra 1

### Course: Algebra 1>Unit 5

Lesson 3: Writing slope-intercept equations

# Slope-intercept equation from graph

Learn to write equations in slope-intercept form for three different lines. Created by Sal Khan.

## Want to join the conversation?

• can someone please explain linear equations? •  All that the slope-intercept form (the equation to describe linear equations) is, is an equation (y=mx+b) where m (the number that multiples x) is the slope and b (the number that is not multiplying a variable on the right-hand side of the equation) is the y-intercept. The x and the y don't really do anything in this case so you can ignore them. An easy way to see this equation is y=(the slope)x+the y-intercept. Hope this helps!
• Why does "b" represent the y-intercept? Did someone just choose a random letter to represent it? Who chose what the y-intercept would be represented by? •  I think it's because y and b are both the second letter in the oft used groups: a, b, c, and x, y, z. b is the point on the line that falls on the y-axis, but we can't call it 'y' so we call it 'b' instead.
Some of this is pretty arbitrary. I'm working with a system right now that calibrates using slope and intercept, and for whatever reason we call them 'm' and 'n' (iNtercept?).
At this point don't get too hung up on the deeper meaning behind the letters (I honestly never thought about why they used 'b' until you asked, and I've taken calculus) and focus on what they represent. It's like learning English; you can explore the deeper meaning of WHY a pig is called a pig, but when you're starting out, it's enough to know that it's spelled p-i-g and represents a farm animal. The deeper meaning can wait until you are studying agriculture.
Hope it helped.
• I don't get it, how does B= 4/3 on A? • Because the slope is -2/3, so when the `x` value increases by one, the y-value decreases by 2/3. That's why moving from an x-value of -1 to 0 will move you down by 2/3 (from a y-value 2 to 4/3, because 2 - 2/3 is 4/3. This can also be written as 6/3 - 2/3 = 4/3)

Another way to do this is by plugging the slope and a point to the slope-intercept equation (y = mx + b) to solve for the y-intercept. I'll use the point (-1, 2).
y = mx + b
2 = -2/3(-1) + b
2 = 2/3 + b
2 - 2/3 = b
4/3 = b
• What would you do if you had something like x=0? or y= -5 • I would like to give a little advice to anyone who needs it for khan academy. In one tab, I keep the video for the lesson. In the other tab, I keep the questions, and complete them while watching the video. Just a little advice that really works well for me. Have a great day! • Can someone summarize the main points of this video? It's kind of confusing! • Ok yes I understand this, but what does it have to do with linear equations on a graph, yes, I know how to find the slope and the y-intercept and how to take slope intercept form and make a graph, but say you have a problem like 5y=-45,which in this case does not have a x so you would have to divide by five in which y would then equal -9 so then my question is how would you plot that on a graph? Because I have tried many times and am getting the right y intercept but not the right coordinates. Thank you for your time -Tj • Isn't negative number in denominator incorrect? • It's not the preferred place for the sign.
The preferred placement for a sign in a fraction is in front of the fraction (not in the numerator or denominator.
For example: -(1/2) = (-1)/2 = 1/(-2). The preferred form would be -(1/2)
Hope this helps.  