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### Course: 8th grade (Eureka Math/EngageNY) > Unit 4

Lesson 3: Topic C: Slope and equations of lines- x-intercept of a line
- Intercepts from a table
- Intercepts from a graph
- Intercepts from an equation
- Worked example: intercepts from an equation
- Intercepts from an equation
- Slope & direction of a line
- Intro to slope
- Slope formula
- Worked example: slope from graph
- Slope of a line: negative slope
- Slope from graph
- Worked example: slope from two points
- Slope of a horizontal line
- Slope from two points
- Intro to slope-intercept form
- Slope-intercept intro
- Slope from equation
- Graph from slope-intercept equation
- Graph from slope-intercept form
- Slope-intercept equation from graph
- 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 from a table
- Converting to slope-intercept form
- Slope-intercept form problems
- Proving slope is constant using similarity
- Intro to point-slope form

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# Intercepts from a table

The y-intercept is the y-coordinate when x=0, and the x-intercept is the x-coordinate when y=0. The y-intercept is not in the table. Since the table represents a line, there's a constant rate of change of y with respect to x. So we can find that pattern and fill in skipped values from the table to find the y-intercept. Created by Sal Khan.

## Want to join the conversation?

- The thing is, it's easy to understand here, but when you actually start the practice, it's totally different.(113 votes)
- SAL's question, -2,8 1,2 2,0 4,-4

MY question 135,96 34,68 56,34 -96,-87

(Not a real question BTW. just emphasizing)(31 votes)

- What is function? We did not learn about it yet.(24 votes)
- A function is a rule where each input is assigned to one, and only one, output. There are many kinds of functions; even the rule "Assign every word to the number of syllables it has" is a function.

But the kind of function we are talking about here is a line. In a graphed line, each x corresponds to only one y. Also the rate of x change to the rate of y change is the same (because it is straight).

So you can use this rule to determine intercepts in a line.

For more on functions, see https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:functions/x2f8bb11595b61c86:evaluating-functions/v/what-is-a-function.

Hope this helps!!(14 votes)

- Is there any way to find intercept x ( or y) if we cannot get the other intercept to zero by following the table method?

In all the questions, if we need to find intercept x/y, the other intercept always perfectly reaches to zero.(6 votes)- If the table doesn't directly go to 0, you could always get the equation of the line described by the table and then plug in 0 for x to get the y-int, or 0 for y to get x-int. To get the equation of a line from a table, you need to determine the slope of the line by calculating the ratio of the change in y-value to the change in x-value. For example, if two points in the table were (1, 2) and (4, 8), you could see that the y value changed by 6 and the x value changed by 3. This would give you a slope of 2 through 6 / 3 = 2. You can then plug a data set for a point into the linear slope-intercept equation: y = mx + b. Going with the numbers from the previous example, let's say I plugged in (1,2). Since m is the slope, my equation would look a little something like this:

2 = 2*1 + b

From there, we can solve for b, and see that b = 0:

2 = 2 + b

2 - 2 = 2 + b - 2

0 = b

Since b is 0, our completed equation looks like this:

y = 2x + 0

To find the intercepts of this equation, we just substitute a 0 in the right place. To find the y-intercept, plug in a 0 for x:

y = 2*0 + 0

y = 0

And for the x-intercept:

0 = 2x + 0

0/2 = 2x/2

0 = x

Hope this helped!(36 votes)

- What if there is a straight line and it never passes through one of the axis? Just curious.(2 votes)
- It really depends on the slope. When the slope is zero, the line is horizontal and there is no x-intercept (but then sometimes the line is right over the axis). If the slope is undefined, there is no y-intercept.(14 votes)

- so what about the x- intercept also that is being asked in the practice intercept from a table......(7 votes)
- Well its pretty much the same thing, you're just solving for X instead of Y.(5 votes)

- i am confused at2:21. why does the -1/2 mean?(5 votes)
- As x increases by 1, y decreases by 2. It doesn't matter if the rate of change is -1/2 or 1/-2. They are both the same value.(8 votes)

- What if your table is going down (
*or up*) by a number that will miss zero?

If I have, say, 8 on the x side, but my table is decreasing every 15, then my next input would miss zero and go to -5! What do I do there?

This is implying that the other side cannot be divided by said number.(6 votes)- You might already have an answer by now, but in your case, you would find out the slope, then the equation of the line and then input one pair of coordinates into 'x' and 'y'. Say 'y' is 10. So then it would become: 10=slope*8+b. b is the constant aka y-intercept which is what we need to find. So then you would solve for b.

Hope that helped!(2 votes)

- Why is it when the line crosses y it is the y-intercept?? why dont we just call it "the time the line crosses the y-axis?"(2 votes)
- An easy way to think about it is, the line is "intercepting the axis at that point." Like a football player intercepting a pass, he or she must cross the path of the ball to intercept it at a certain point.(12 votes)

- How do you find the x and y intercepts with just random coordinates they give you? For example, they gave me (-15, 5), (-9, 10), and (-3, 15). That's all they gave me! Those are random coordinates to a line! Am I supposed to fill in the blanks myself??(4 votes)
- In reality, you only need 2 of these points. The first step is to find the slope which is (y2-y1)/(x2-x1) and you can use any of these points. Next write the equation is point slope form which is y-y1=m(x-x1) using the slope and one of the points. Then you can simplify to write this is slope-intercept form and solve the x and y intercepts as given. Remember these coordinates are not random as they are all on the same line!(5 votes)

- what does that triangle symbol mean when he says "change in y over change in x"

Please explain

Thank you(3 votes)- The triangle is the Greek letter Delta which is commonly used as an abbreviation for "change in".

Delta Y / Delta X is just another shorter way of writing Change in Y / change in X.(6 votes)

## Video transcript

The following table
of values represents points x comma y on the
graph of a linear function. Determine the y-intercept
of this graph. So just as a reminder of
what the y-intercept even is, if you imagine a linear function
or a line if we're graphing it, if we imagine a
line, so let's say that is our line
right over there. This is our y-axis. This is our x-axis. The y-intercept is where
we intersect the y-axis. Now, what do we know
about the y-intercept? Well, at the y-intercept x
is going to be equal to 0. So this is the point
0 comma something. And so when people
are talking about, what is your y-intercept? They're usually
saying, well, what is the y-coordinate
when x equals 0. So we're really
trying to figure out, what is the y-coordinate
when x equals 0? So we know the x-coordinate
when y is equal to 0. So this is actually
the x-intercept. So this point right over
here is the point 2 comma 0. So when people say
x-intercept, that's the x-coordinate
when y equals 0. Well, they gave us
the x-intercept. So that right over there
is the x-intercept. But what's the y-intercept? What is the y-value
when x equals 0? Well, let's see. They give us what happens to
y when x is negative 2, when it's 1, when it's
2, when it's 4. So maybe we can backtrack
from one of these to get back to what happens
when x is equal to 0. So let me rewrite this table
so I can give ourselves a little bit more
breathing room. So let's say we have
x and we have y. x and y. And they already tell us that
when x is negative 2, y is 8. And I actually want
to think about what happens when x is
negative 1, when x is 0. Then they tell us
when x is 1, y is 2. When x is 2, y is 0. This right over here
is the x-intercept. When x is 4, y is negative 4. So they skip 2 right over
here. y is negative 4. So let's just see how y changes
with respect to changes in x. So when we go here, when x
changes by 1, y goes down by 2. And it's a line, so
it's going to have a constant rate of change
of y with respect to x. So similarly, when
x increases by 1, y is going to decrease by 2. So y is going to be 6 here. When x increases by 1 again,
y is going to decrease by 2. So we're going to get to 4. And we see it works. Because if we
increase by 1 again, then it is indeed the case
that y decreased by 2. And you see here when
we increase x by 2, then y decreases
at twice the rate. Because now we didn't
just increase by 1, we increased by 2. So now y is going
to decrease by 4. And what's constant
here is your change in y over your change in x. When x increases by
1, y decreases by 2. When x increases by
2, y decreases by 4. Either way you think
about it, your change in y for a unit
change in x is going to be equal to negative 2. But anyway, we actually
answered the question before without even
realizing it when we filled in all
of these values. What is the y-value
when x equals 0? Well, the y-value is 4. So the y-intercept here is 4. We didn't really
graph this to scale. It would actually look a
little bit more like this if we were to try to
graph it properly. So this right over here is 4. This right over here is 2. And our line looks
something like this. Our line will look
something like that.