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## Algebra 1

### Unit 4: Lesson 4

x-intercepts and y-intercepts# Intercepts from a table

CCSS.Math: , ,

Sal finds the y-intercept of the graph of a linear function given a table of values. 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.(85 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)(12 votes)

- What is function? We did not learn about it yet.(2 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!!(11 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.(5 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!(3 votes)

- how do I solve a graphing question with no graph(3 votes)
- The same way Sal did; you can use an input and output function.(2 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??(3 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!(2 votes)

- I have a question, do all graphs have an x-intercept?(2 votes)
- Not at all! If you look at the graph of the function y=2 you will see that is is a horizontal line and does not have a x intercept(4 votes)

- Δx and Δy are not constant in my test :((3 votes)
- Then it cannot be a linear equation, Not seeing the question, do not know if you have an error or not.(2 votes)

- i divided 15 by 7 to get what i should multiply -7 by to get -15, did it not work because i simplified it to the first two digits or because i did something else incorrect?(3 votes)
- You should be subtracting as shown in the video. Each value in the table is subtracted with the prior value to find the common change for X and also for Y.(2 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.(2 votes)- Then it's not proportional. That doesn't really make any major difference.(1 vote)

- What if there is a straight line and it never passes through one of the axis? Just curious.(2 votes)
- There are an infinite number of lines that only intersect one axis. If x = n where n is a real number then it is a straight line that is vertical and parallel to the y-axis (or is the y-axis) and only crosses the x-axis. Its slope is undefined. If y = n then it is a horizontal line that is parallel to the x-axis (or is the x-axis) and only intersects the y-axis. Its slope is zero.(2 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.