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

Lesson 11: Extra practice: Intercepts# Intercepts from an equation

Let's graph -5x + 4y = 20 from its intercepts. Intercepts are the places where a line crosses the x- and y-axes. When a line crosses the x-axis, the y value is 0. That's the x-intercept. When a line crosses the y-axis, the x value is 0. That's the y-intercept. The line passes through those points. Created by Sal Khan and Monterey Institute for Technology and Education.

## Want to join the conversation?

- I am a 7th grader in Algebra I and we just started intercepts. One of the questions we had to answer was, Find an equation for the line described has x intercept 2 and y intercept 5. how would you do that?(128 votes)
- The points of the intecepts are (2,0) and (0,5). to find the equation of the line, you need to put it into slope-intercept form which is y=mx+b, where m is the slope and b is the y intercept. to find the slope you do 5-0 where you subtract the second y (5) from the first y (0). you put that over 0-2, where you subtract the first x (2) from the second x (0). your slope should look like this 5/-2.

once you have your slope your equation should look like this,

y=5/-2+b. to find b, you just put in the y intercept. the equation is

y=5/-2+5(120 votes)

- is Y always = to 0?(21 votes)
- Y is always = 0 to find X-intercepts.

X is always =0 to find Y-intercepts.(97 votes)

- I'm a little confused I attempted this question from the next practice section:

Determine the intercepts of the line.

−4x+7=2y-3

And I came up with y= (0, -5) x= (2.5, 0)

and when I entered my answer it told me it was incorrect and I looked at the hint and it seems like they wanted the same coordinates just with positive numbers instead.

Is there a reason for that, for instance if I were taking the TASC do you think they'd accept my answer as well?

I remember reading there is basically an infinite amount of answers for Linear Equations, I'm just curious as to if I computed it on my own wrong or just an awkward way.

I did this:

-4x+7=2y-3

-7 -7

-4x = 2y -10

then

4(0) = 2y = 10

-10/2y = -5

y = -5

and

-10/-4 = 2.5

Sorry for the awful formatting my keyboard/ computer is all but completely broken(23 votes)`-10/2y = -5`

When you're dividing, you don't reverse the sign. It should be`2y - 10 = 0`

`+10`

to both sides`2y = 10`

divide both sides by**positive 2**(because the sign doesn't change as we're dividing)`y = 10/2`

and finally:`y = 5`

Any other questions? Feel free to comment me back!(24 votes)

- My question is more from experience. I am a 70 year old, taking this for a refresher. I know I have the right answer since I have attended a university in the field Electrical Engineering and Computer Science. However, I didn't get the problem right or wrong. The problem is how the computer accepts the answer. Do I have to enter the answer as a decimal, or a fraction? Please help since neither answer gave me the correct solutiopn. i.e. 3/4, 6/8, .75(15 votes)
- Hi Mr Mellow, I'm not sure of which questions you did, but certain questions would have certain formats for the answers. Some questions would want you to write the answer as a decimal, or another question would want you to type it as a fraction.(16 votes)

- What if you have a repeating decimal in your intercept? What can you do to avoid it?(13 votes)
- An intercept can be any real number: an integer, a fraction, a mixed number, a decimal.

In the case of a repeating decimal, I would keep the number as a fraction rather than changing to a decimal. It's an easy way to keep the entire value of the intercept.(13 votes)

- I am unsure whether there is a quicker way to find out the intercepts. I know that if you have a line equation that is like

y=2x+3 that the y-intercept is (0,3)

But is there a quick way for the x-intercept like this with any particular types of linear equations?(12 votes)- There may be a faster way, but it is fairly quick and certain when you begin the y-intercept (0,3) and plot points based on the slope [rise 2, run 1 => (1, 5), (2, 7) or reverse (-1, 1), (-2, -1)].

I usually plot three points and draw a line through them to find the x-intercept (-1.5, 0).(4 votes)

- I am a 9th grader at Whittier high school doing algebra 1, we are reviewing how to get Intercepts from an equation. One of the questions given is a little confusing for me and a few of my classmates. How would I get the X and Y intercepts from this? y−6=4(x+5)(5 votes)
- To get the X intercept plug in 0 for y so: 0-6=4(x+5)

Then solve for x the x intercept will be (-6.5, 0)

To get the Y intercept plug in 0 for x so: y-6=4(0+5)

then solve for y, the y interpect will be (0, 26)

I'm pretty sure, I hope this makes sense I can explain it in more depth if necessary.(16 votes)

- if the x intercept is 2 and the y intercept is -1 what is the slope of the corresponding line?(6 votes)
- I can't seem to understand this at all, the video doesn't seem to explain everything, can someone please explain this to me in layman's terms?(6 votes)
- An intercept is on the axis, so it will always have a 0 somewhere, the x intercept has y=0, so the point will be (#,0), and the y intercept has x=0, so the point will be (0,#). So given any equation, 3x + 4y = 24, we can find the x intercept by setting y=0, so we do 3x+4(0)=24 which gives 3x=24, then divide by 3 to get x=8. For y intercept, set x=0, 3(0)+4y=24, 4y=24, and divide by 4 to get y=6. Does this help?(5 votes)

- How do you know which point to plot first. In the last quis I had the right coordinated but in a different order.(4 votes)
- Ordered pairs are always in the form (x-value, y-value). Make sure you put the right value in its place. And make sure you move left/right for X and up/down for Y.(8 votes)

## Video transcript

We have the equation negative 5x
plus 4y is equal to 20, and we're told to find the
intercepts of this equation. So we have to find the
intercepts and then use the intercepts to graph this line
on the coordinate plane. So then graph the line. So whenever someone talks about
intercepts, they're talking about where you're
intersecting the x and the y-axes. So let me label my axes here, so
this is the x-axis and that is the y-axis there. And when I intersect the x-axis,
what's going on? What is my y value when
I'm at the x-axis? Well, my y value is 0, I'm not
above or below the x-axis. Let me write this down. The x-intercept is when y
is equal to 0, right? And then by that same
argument, what's the y-intercept? Well, if I'm somewhere along the
y-axis, what's my x value? Well, I'm not to the right or
the left, so my x value has to be 0, so the y-intercept occurs
when x is equal to 0. So to figure out the intercepts,
let's set y equal to 0 in this equation and solve
for x, and then let's set x is equal to 0 and
then solve for y. So when y is equal to 0, what
does this equation become? I'll do it in orange. You get negative 5x plus 4y. Well we're saying y is 0, so
4 times 0 is equal to 20. 4 times 0 is just 0, so we
can just not write that. So let me just rewrite it. So we have negative
5x is equal to 20. We can divide both sides of this
equation by negative 5. The negative 5 cancel out,
that was the whole point behind dividing by negative 5,
and we get x is equal to 20 divided by negative
5 is negative 4. So when y is equal to 0, we
saw that right there, x is equal to negative 4. Or if we wanted to plot that
point, we always put the x coordinate first, so that
would be the point negative 4 comma 0. So let me graph that. So if we go 1, 2, 3, 4. That's a negative 4. And then the y value is
just 0, so that point is right over there. That is the x-intercept, y
is 0, x is negative 4. Notice we're intersecting
the x-axis. Now let's do the exact same
thing for the y-intercept. Let's set x equal to 0, so if
we set x is equal to 0, we have negative 5 times 0 plus
4y is equal to 20. Well, anything times 0 is
0, so we can just put that out of the way. And remember, this was setting
x is equal to 0, we're doing the y-intercept now. So this just simplifies
to 4y is equal to 20. We can divide both sides of this
equation by 4 to get rid of this 4 right there, and you
get y is equal to 20 over 4, which is 5. So when x is equal to
0, y is equal to 5. So the point 0, 5 is on the
graph for this line. So 0, 5. x is 0 and y is 1, 2, 3,
4, 5, right over there. And notice, when x is 0, we're
right on the y-axis, this is our y-intercept right
over there. And if we graph the line, all
you need is two points to graph any line, so we just have
to connect the dots and that is our line. So let me connect the dots,
trying my best to draw as straight of a line is I can--
well, I can do a better job than that-- to draw as straight
of a line as I can. And that's the graph of this
equation using the x-intercept and the y-intercept.