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### Course: 8th grade > Unit 3

Lesson 3: Intercepts# Worked example: intercepts from an equation

Let's find the x- and y-intercepts of the equation 2y + 1/3x = 12, where a line crosses the x-axis (the x-intercept) and the y-axis (the y-intercept) on a graph. To find the x-intercept, we make y equal to 0 and solve the equation for x. To find the y-intercept, we make x equal to 0 and solve for y. Created by Sal Khan and Monterey Institute for Technology and Education.

## Want to join the conversation?

- I know in the equation y=mx+b, b is the y-intercept. Is there a x-intercept in another slope equation? Thanks!(8 votes)
- Slope intercept form is y=mx+b. Really, it is more like "Rise/Run Slope of a line from the y-intercept form". If you want to know the x-intercept form you can solve the equation for x.

y=2x+4 would become x=1/2y-2. Now plug in zero for y and you will have what x is equal to (-2). The reason we use y=mx+b is because the idea of rise/run no longer works correctly in this version of slope x-intercept. You have run/rise instead of rise/run. This is unwanted confusion as now you have

y=mx+b "Rise/Run Slope of a line from the y-intercept form"

and

x=my+b "Run/Rise Slope of a line from the x-intercept form"

I hope this helped you find the x-intercept and also why we only use y-intercept slope formulas.(10 votes)

- Need help, what do the "|" mean in an equation? Example, y=|x-2|

Thanks(6 votes)- those are called absolute value bars, no matter what is inside the absolute value bars, it comes out as positive. So, for example |4| = 4 and |-4| = 4.(8 votes)

- How do you find intercepts when the formula is more complex as in y=x*sqrt(16-x^2)(7 votes)
- The general rule of thumb for finding intercepts is to plug 0 in for the other number. To finish the equation you provided, you would need to use the zero-product property to set each piece equal to zero and solve..(6 votes)

- So, if you wanted to do the same (figure out the x and y intercept) for any other equation, should I only use 0 as a substitute to figure them out? Would it be the same if you used other numbers as substitutes?(6 votes)
- Katie, yes, exactly. If the equation is in standard form:ax+by=c then you just set x equal to 0 to find the y intercept and set y equal to 0 to find the x intercept. It makes sense, right. The y intercept is when the line crosses the y axis, so x will always be 0, so that is why we set x equal to 0. To find where the line crosses the y axis.

The same logic applies when finding the x intercept, set y equal to 0 to find where the line crosses the x axis, because y will always be zero at the x intercept.

Ex: (0,8) y intercept, notice x is 0

(2,0) x intercept notice y is 0(7 votes)

- Is there a rule governing linear coordinates that pass the exact centre of the graph?

For instance, where Xintercept=Yintercept=0...

Since you can't draw a linear graph from using just one point, what can we do with such information?

I understand a lot of formulas will meet with the centre, and the lines can angle 360degrees,

through all quadrants of the graph when it does.

But is it some type of typical linear graph? Or is there special methods involved?

What can we know about situations that don't work while originally meeting the demands for the X/Yintercept method? (crossing both x0 and y0, being a linear equation etc.)

Perhaps it is a singular exception?

Sorry for this weakly translated and confusing question.

I'd like to hear anything people got to say about this.(6 votes)- When linear coordinates pass the exact centre of the graph, i.e. x-int=y=int=0; you cannot draw a line just based off this information due to the fact that it is quintessential that you have or know a minimum of 2 points in order to graph the line. Factors of a line which will help in this scenario will include; the gradient, the equation of the line and even just simple another point. Hope this helps!(5 votes)

- How do answer questions about slope in word problems? That is my problem on math test with any unit.(7 votes)
- Can X and Y be negative(3 votes)
- Simple answer, Yes(2 votes)

- this doesn't relate to this vid at all but dividing anything by zero is so random like 1/0.0001=10000 and 1/0.000000=1000000. so does that mean 1/0 is infinity?(3 votes)
- What you're doing is doing
`1/x`

when`x`

is approaching`0`

. If`1/0`

were to have a value, this is a totally valid way to go about it, BUT we have to see if the result is the same whether approaching from the positive side or the negative side.

Problem is you're only approaching it from the positive side and haven't checked the negative side yet!

Ok! If we make`x`

approach`0`

from the negative side in the same manner, we get`1/-0.1 = -10, 1/-0.01 = -100, 1/-0.0001 = -10000, ...`

. As you can see, the value of`1/x`

is getting larger and larger on the negative side, so it's approaching negative infinity.

Hold on.

- When we evaluated`1/x`

as`x -> 0+`

, it approached*positive*infinity.

- When we evaluated`1/x`

as`x -> 0-`

, it approached*negative*infinity.

So, does`1/0 = infinity`

?(2 votes)

- How do you work out the intersections of y=x^2 and y=3x+18(3 votes)
- Do you mean "intersections" as points where the
`2`

graphs meet?

Well then, set them**equal**to each other; at an intersection, the`y`

s are equal at the`x`

value, if that makes sense.`y = x^2`

,`y = 3x + 18`

Equation of interest:`x^2 = 3x + 18`

Then, solve for the`x`

-coordinates of the points of intersection:`x^2 - 3x - 18 = 0`

(I'll use factoring)`(x + 3)(x - 6) = 0`

(setting each factor equal to`0`

)`x + 3 = 0 => x = -3`

`x - 6 = 0 => x = 6`

Now the`x`

-coordinates of the points are`x = {-3, 6}`

. Finally, plug them into either equation to get their respective`y`

-coordinates. I'm choosing the`y = x^2`

equation.`x = -3: y = (-3)^2 = 9`

`x = 6: y = (6)^2 = 36`

Therefore, the intersections of`y = x^2`

and`y = 3x + 18`

are:`{(-3, 9), (6, 36)}`

.

Hope it helped!(0 votes)

- When you're asked to make your own equation (ex. 2y+3x=12) how do we figure out what the 2y+3x equal to. Like the number after the equal sign is that the y-intercept or the slope or something else?(2 votes)
- EX: Find the X intercept when 2Y+3X=12. The Y value automatically equals zero because you are looking for the X value when X is directly on the X axis(or when Y is equivalent to zero). 2Y(0)+3X=12. 0+3x=12. 3x=12.

X=4 when Y=0(AKA the value of X is four when you're looking at where the X axis and your X value meet, which means that your Y can be no greater or lesser than zero)(1 vote)

## Video transcript

We're told to find the x- and
y-intercepts for the graph of this equation: 2 y plus
1/3x is equal to 12. And just as a bit of a
refresher, the x-intercept is the point on the graph that
intersects the x-axis. So we're not above or below
the x-axis, so our y value must be equal to 0. And by the exact same argument,
the y-intercept occurs when we're not to the
right or the left of the y-axis, so that's when
x is equal to 0. So let's set each of these
values to 0 and then solve for what the other one has
to be at that point. So for the x-intercept,
when y is equal to 0, let's solve this. So we get 2 times 0, plus
1/3x is equal to 12. I just set y is equal to
0 right there, right? I put 0 for y. Well, anything times 0 is just
0, so you're just left with 1/3x is equal to 12. To solve for x, you can think of
it as either dividing both sides by 1/3, or we can multiply
both sides by the reciprocal of 1/3. And the reciprocal of 1/3 is 3,
or you can even think of it as 3 over 1. So times 3 over 1. And so we're left with 3 times
1/3, that just cancels out, so you're left with x is equal
to 12 times 3, or x is equal to 36. So when y is equal
to 0, x is 36. So the point 36 comma 0 is on
the graph of this equation. And this is also the
x-intercept. Now, let's do the same thing
for the y-intercept. So let's set x equal 0, so you
get 2y plus 1/3, times 0 is equal to 12. Once again, anything
times 0 is 0. So that's 0, and you're just
left with 2y is equal to 12. Divide both sides by 2 to solve
for y, and you're left with y is equal to
12 over 2, is 6. So the y-intercept is when
x is equal to 0 and y is equal to 6. So let's plot these
two points. I'll just do a little hand-drawn
graph, and make it clear what the x- and the
y-intercepts are. So let me draw-- that's my
vertical axis, and that is my horizontal axis-- and we have
the point 36 comma 0. So this is the origin right
here, that's the x-axis, that's the y-axis. The point 36 comma 0 might
be all the way over here. So that's the point
36 comma 0. And if that's 36, then the
point 0, 6 might be right about there. So that's the point 0, 6. And the line will look
something like this. I'm trying my best to draw
a straight line. And notice where the line
intercepted or intersected the y-axis, that's the y-intercept,
x is 0, because we're not to the right
or the left of it. Where the line intersected the
x-axis, y is 0, because we're not above or below it.