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## 8th grade (Illustrative Mathematics)

### Course: 8th grade (Illustrative Mathematics) > Unit 3

Lesson 8: Extra practice: Slope# Worked examples: slope-intercept intro

CCSS.Math:

Worked examples practicing the relationship between slope, y-intercept, and linear equation in slope-intercept form.

## Want to join the conversation?

- I learned that the slope is the change in y over the change in x, like: y/x. Hope this helps.(7 votes)

- How exactly do you know how a slope as a fraction is a positive or negative?(8 votes)
- You would know if the slope is negative if the (-) is placed before your fraction. Visually graphing, it would look like a downhill slope.

Likewise, when the fraction is positive, graphically speaking it'll look like it is going on a forever uphill slope.

Negative: Going left to right --> down

Positive: Going left to right --> up(3 votes)

- what is life meant to be?(7 votes)
- i learnt the equation as y=mx=c does it make a difference?(3 votes)
- Just note that it is not always the same value as the C in standard form, Ax + By = C(10 votes)

- But what if m = 0 and x = a whole number?(4 votes)
- Solomon.If the equation is y=mx+b,and M is 0.The equation will be 0x+b.Because a number time 0 is 0,y will equal the slope intercept in a line that is perfectly horizontal(4 votes)

- What is the y-intercept of y=4x, equals, 4, x?(4 votes)
- Well then when x is 0(y intercept) y is zero as well. The intercepts are the origin. The formula is y=4(slope)x+0(y value of y intercept)=4x(2 votes)

- how to complete the equation of the line whose slope is -2 and y-intercept is (0,3)?

y=?(3 votes)- the answer would be y=-2x+3

y=mx+b the m is the slope and the b is the y-intercept(2 votes)

- if y=4 and b=4 that means that y=b?(3 votes)
- If y=4, that means that the slope is 0 and b=4, so it is not the fact that they are both equal to 4, it is that the first one leads to the second one. This is a horizontal line through y=4.(4 votes)

- he says that he makes the mistake of putting y=y=5x+4, but isn't that the same thing?(3 votes)
- It is the same thing - he just means that when you input your answer, don't put the y= in front because it'll mark you wrong.(3 votes)

- What exactly is Slope-Intercept form?(3 votes)
- Slope-intercept form is a way of writing a linear equation. The slope-intercept form is written as y = m*x + b where m is the slope of the line and b is the y-value where the line intersects the y-axis.(3 votes)

## Video transcript

- [Sal] Let's do some practice examples from our intro to slope
y intercept exercise. What is the slope of y is equal to negative four x minus three? So you might already recognize, this is in slope intercept form. Just as a reminder,
slope intercept form is y is equal to mx plus b, where the coefficient on
this x term right over here, that is our slope, and then this constant right over here, that is going to give
you your y intercept. So if they're saying,
what is the slope here? Well I just need to figure out, what is the coefficient on this x term? And you can see that the coefficient here is a negative four. So that is going to be our m, that is going to be our slope. Now just as a reminder,
you have to make sure that it's solved in this way, that is is solved for y, y is equal to something
times x minus three, so that's our slope. Let's do another one of these. So we're asked, what is the y intercept of y is equal to negative
three x minus two? So once again we already have
it in slope intercept form. It's already been solved for y. It's of the form y is equal to mx plus b, where m, our slope, is
given right over here, negative three. But they're not asking for our slope, they're asking for the y intercept. Well the y intercept is given by b here, so b is negative two. Pay close attention to the sign here. So b is equal to negative two. But when I look at these choices, I don't see a b is equal to negative two, so what are they talking about? Well a y intercept is, what is the y value
when x is equal to zero? And you could see that here, if x was equal to zero
then that term goes away and y is equal to b. So if you want to know the point where the graph described by this equation intercepts the y axis, well it's going to be what
is y when x is equal to zero? Well when x is equal to zero,
y is equal to negative two. And you could see that in
our original equation, again. If x were zero, this term would go away, and y would be equal to negative two. So zero, comma, negative two. So it would be that
choice right over there. On Khan Academy obviously you
just have to click on that, you don't have to shade it in. Let's do one more. Complete the equation of the
line whose slope is five, and y intercept is zero, comma, four. So once again the general form is y is equal to our slope times x, if I want to put it in
slope intercept form, plus our y intercept. Well they're telling
us, our slope is five. Whose slope is five. So we know that m is going to be five. And they tell us that the
y intercept is zero, four. So the y intercept, b,
that is the value of y when x is equal to zero. So the value of y when x equals zero is this four right over here. So that is going to be four. So I could say y is equal to five times x plus four. And when you're actually
entering it on Khan Academy, you would just type it in, or if you're using the app you would use it with your finger. And I always make the
mistake of writing y equals, and I type in y equals five x plus four. Notice they already gave you
the y equals right over there. That's all you have to do, recognize the slope, the y intercept, and then remember what the slope
intercept form actually is.