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## Algebra 1

### Course: Algebra 1 > Unit 5

Lesson 1: Intro to slope-intercept form# Slope and y-intercept from equation

CCSS.Math:

In an equation in slope-intercept form (y=mx+b) the slope is m and the y-intercept is b. We can also rewrite certain equations to look more like slope-intercept form. For example, y=x can be rewritten as y=1x+0, so its slope is 1 and its y-intercept is 0.

## Want to join the conversation?

- Where am i gonna need to know slope(37 votes)
- u need to know this in 8th grade(17 votes)

- is the y intercpet when it touch the line.(5 votes)
- Wording is important here. The y-intercept is where the line crosses the y-axis (touches the y-axis).

Great question. Hope this helps. <|:)(10 votes)

- you dint answer any of them you just did the equation how am i suposed to put the peices together(5 votes)
- I'm not completely sure what you mean, but I'll try to explain as best as I can:

You're not supposed to solve the equation for y=mx+b. For y=mx+b is more like plugging in the numbers to help you draw a graph and identify points. For example, if you have the equation y=5x+8, you would use a graph to identify the points, you would use the rise over run method for this. Let's say a point is 2,18. x=2 and y=18. To check if this is correct you would solve the equation as shown.

18=5(2)+8, 18=10+8, 18=18.

The equation is like a puzzle for you to solve and fill in the missing pieces.

I hope this helps!(8 votes)

- I don't understand would the y intercept be the reciprocal?(4 votes)
- How would this equation be graphed on a graph??

y = -14 + -10(3 votes)- Thou must think 2 dimensionally. Thou art solving for y, without an x. Furthermore, thou havest infinite x values so thy graph shall be a straight line at the y value of -24(5 votes)

- I have a question, so what if there is a =n equation y=4.5x, we found the slope, but where is the y intercept?(5 votes)
- I have a math equation and it says "Amy charges $100 for 8 hours of tutoring" This is a direct variation and how would I know which is the {X} and would it be like this y=100x+8 do we know if it is {+,-,/, and X} which one would make sense...pls help me I am so confused.(2 votes)
- why is this important(3 votes)
- There are many real-life examples of lines that would be in slope-intercept form. It moves from theory to practical in many fields of study as well as in many things you do on an almost daily basis even though you might not realize it.(2 votes)

- Can m=my+b solve for the x intercept?(2 votes)
- Good question.

To find the x-intercept we generally just use the same formula 'y=mx+b'. The reason that 'b' is the y-intercept is because at the 'y-axis, x=0'. By this I mean if you look at any graph, for the point a line touches the y-axis, the x-value of a coordinate is always = 0.

Knowing this, if you substitute 0 in for x in the formula you get:

'y=mx+b' -> 'y=m(0)+b'.

So 'y (intercept)=b'. That's why the y-intercept is b.

Now consider the x-intercept. At the x-intercept, the y value for a point is always 0, 'At the x-axis, y = 0.' So sub 0 in for y and you get:

'y= mx+b' -> '0=mx+b' -> '-mx=b' -> 'x (intercept) =-b/m'. So the x-intercept is -(y-intercept)/slope.

Hope this helps.(3 votes)

- If the y intercept in an equation is equal to zero, woudlnt the slope of the entire line be zero? Or would the points labeled by the equation make up the slope?(2 votes)
- If the y intercept of a linear equation is 0, then you also know the x intercept is 0. This just tells you that it is a proportional relationship. The slope (called k for proportional relationships) would be given by k=y/x for any point on the line. It would only be 0 slope if one of the other points was (x,0) where x could be any number except 0. As an example, if it goes through a point (6,4), the slope (or constant of proportionality) would be 4/6=2/3, so equation would be y = 2/3 x.(2 votes)

## Video transcript

- [Instructor] What I'd
like to do in this video is a few more examples recognizing the slope and
y-intercept given an equation. So, let's start with something that we might already recognize. Let's say we have something of the form y is equal to five x plus three. What is the slope and the
y-intercept in this example here? Well, we've already talked about that we can have something
in slope intercept form where it has a form y
is equal to the slope, which people use the letter m for, the slope times x plus the y-intercept, which people use the letter b for. So, if we just look at this, m is going to be the coefficient
on x right over there. So, m is equal to five. That is the slope. And b is just going to be this
constant term, plus three. So, b is equal to three. So, this is your y-intercept. So, that's pretty straightforward but let's see a few slightly
more involved examples. Let's say if we had
form y is equal to five plus three x, what is the slope and the
y-intercept in this situation? Well, it might have
taken you a second or two to realize how this earlier equation is different than the one I just wrote. Here, it's not five x, it's just five, and this isn't three, it's three x. So, if you wanna write it in the same form as we have up there, you can just swap the
five and the three x. It doesn't matter which one comes first, you're just adding the two, so you can rewrite it as y is
equal to three x plus five. And then it becomes a little bit clear that our slope is three, the
coefficient on the x term, and our y-intercept is five, y-intercept. Let's do another example. Let's say that we have the equation y is equal to 12 minus x. Pause this video and see if
you can determine the slope and the y-intercept. All right, so, something
similar is going on here that we had over here. The standard form, slope intercept form, we're used to seeing the x
term before the constant term, so we might wanna do that over here. So, we could rewrite this as y is equal to negative x plus 12, negative x plus 12. And so, from this, you
might immediately recognize, okay, my constant term, when it's in this form, that's my b, that is my y-intercept. So, that's my y-intercept
right over there. But what's my slope? Well, the slope is the
coefficient on the x term but all you see is a negative
here, what's the coefficient? Well, you can view negative x as the same thing as negative one x. So, your slope here is
going to be negative one. Let's do another example. Let's say that we had the
equation y is equal to five x. What's the slope and y-intercept there? At first, you might say, hey, this looks nothing
like what we have up here. I only have one term on the right-hand side
of the equality sign. Here, I have two. But you could just view
this as five x plus zero, and then it might jump out at you that our y-intercept is zero and our slope is a
coefficient on the x term. It is equal to five. Let's do one more example. Let's say we had y is
equal to negative seven, what's the slope and y-intercept there? Well, once again, you might say, hey, this doesn't look
like what we had up here, how do we figure out the
slope or the y-intercept? Well, we could do a similar idea. We could say, hey, this is the same thing as y is equal to zero times x minus seven. And so now, it looks just
like what we have over here and you might recognize that our y-intercept is negative seven, y-intercept is equal to negative seven. And our slope is a
coefficient on the x term, it is equal to zero. And that makes sense. For a given change in x, you
would expect zero change in y 'cause y is always negative
seven in this situation.