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### Course: Algebra (all content) > Unit 3

Lesson 7: Writing slope-intercept equations- Slope-intercept equation from graph
- Writing slope-intercept equations
- Slope-intercept equation from graph
- Slope-intercept equation from slope & point
- Slope-intercept equation from two points
- Slope-intercept from two points
- Slope-intercept form problems
- Slope-intercept equation from slope & point (old)
- Slope-intercept equation from slope & point: fractions (old)
- Finding y intercept given slope & point (old)
- Slope-intercept form review

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# Slope-intercept equation from slope & point: fractions (old)

An old video where Sal finds the slope-intercept form of a line that has a slope of ⅓ and goes through the point (-12,-14/3). Created by Sal Khan and Monterey Institute for Technology and Education.

## Want to join the conversation?

- Why is 'b' considered the y-intercept and why is 'y' in y = mx + b(8 votes)
- Armin,

The y intercept is when x=0.

For the equation y=mx+b,

if x = 0 then y=m*0+b so when x=0, then y=b.

So the y intercept is the point (0,b).

I hope that helps make it click for you.(9 votes)

- If the slope is -5/14 and point is -1/2 Is the y intercept 1.642857

Should the answer be a fraction?(5 votes) - i need help on graphing this equation y = 1/4x(2 votes)
- Try applying y = mx + b where m is the slope and b is the y-intercept.

In your equation, m would equal 1/4 and b = 0 (b is not mentioned so it is therefore 0)

If b = 0, we know that the line intercepts the y-axis at 0.

If m = 1/4 then the slope of the line is 4 units across to the right and 1 unit up.

So plot a line that goes through coordinates (0,0) and (4,1) and so on.

Hope that helps. It's hard to explain without a diagram.(3 votes)

- How do I rewrite the equation 6y-5x=11 in slope-intercept form?(2 votes)
- In y=mx+b, what does b represent?(2 votes)
- b is your y-intercept (where the line crosses the y-axis)(1 vote)

- How do you find a slope for a line equation: 3x- 2y= 7(1 vote)
- First write it in the form y = ax + b, where a will be the slope:

3x - 2y = 7;

2y = 3x - 7;

y = (3/2)x - 7/2.

We observe that the slope of the line is 3/2.(3 votes)

- Comment

Sal had the following equation: -14/3 = 1/3(-12)+b above. Instead of dividing by the denominator of 1/3, 3 into 12 to get -4, he should have just multiplied 1/3 times -12 to get -12/3. Than he could have added +12/3 to both sides of the equation, and the terms would have already been in their common denominator form. Sal than had to than reestablish 4 as 12/3 which he already had on the other side. Not a mistake, but an opportunity to keep the terms already in their common denominator form missed(2 votes)- Sal may have done this to show everybody the step-by-step procedures that one might have done.(1 vote)

- I am doing this one problem and it goes like this for a fractional slope:

y=-1/3x-3 can you help me with this one?(1 vote)- I assume you are trying to graph the line (you didn't say).

First, graph the y-intercept (0, -3). Then use the slope to find more points.

You have a negative slope, so you know the line slants down from left to right. When you have a negative slope to use fo graphing, you put the minus on one of the two numbers.

Starting from the y-intercept, you can do either of the following movements to get more points:

(-1)/3 = Go down 1 and right 3

1/(-3) = Go up 1 and left 3

Hope this helps.(2 votes)

- how would I convert the equation 6x-5y=12 into slope intercept form, I tried and I came up with y= 6/5x + 12 but I am not sure if this is correct(1 vote)
- No. that is not correct. You need to divide the 12 by -5 as well.(0 votes)

- How would we use this information is real life?(1 vote)

## Video transcript

Write the equation of the
line that has a slope of 1/3 and contains the point
negative 12, negative 14/3. So the equation of
a line we can write as y is equal to mx plus b. This is in slope-intercept
form, where m is our slope and b right over here
is our y-intercept. And they have actually
given us our slope. Our slope, they tell us, is 1/3. So we know that m
is going to be 1/3. So we know that y is
equal to 1/3 x plus b. And so now we just
have to solve for b. And the way we can solve for
b is that we know this line contains the point
negative 12, negative 14/3. So when x is equal
to negative 12, y is equal to negative 14/3. So let's write that down. Negative 14/3 is going
to be equal to 1/3-- our slope-- times
our x value, which is negative 12-- times
negative 12-- and then plus b. So when x is
negative 12, we know that y is equal
to negative 14/3. And we also know that
the slope is 1/3. That's the m in mx plus b. So now we can just solve for b. The left-hand side-- I'll just
leave it as negative 14/3-- is equal to 1/3
times negative 12. 1/3 times negative
12 is negative 4, so this is negative 4, plus b. Let me write the plus
b in that same color that I had started it with. Plus b. It looks like a yellow color. And now, to isolate b
on the right-hand side, we can add 4 to both sides. I want to get rid
of this negative 4. So let's add 4 to both sides. So plus 4, plus 4-- on
the right-hand side, we're left with just a b. b is equal to-- on the
left-hand side, we have 4. 4 I can rewrite. Because I'm going to have
to add 4 to negative 14/3. So I want a common denominator. 4 is the same thing as 12/3. So 4 is 12/3, minus 14/3. So I just want to be clear. I just rewrote the 4 as 12/3. So 12/3 minus 14/3, or
negative 14/3 plus 12/3, is going to give us-- well, we
have the same denominator of 3. So we're going to have 3. 12 minus 14 is negative 2. So we have negative
2/3 is equal to b. So the equation of the
line we figured out. They gave us the slope. And now we just figured
out the y-intercept using this information
right over here. So the equation of
our line is going to be y is equal to 1/3 x-- we
got the 1/3 from the problem-- plus b. b is negative 2/3. So I could just write minus 2/3. And we are done.