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## 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 an equation

CCSS.Math: , , , , ,

Sal finds the x and y-intercepts of -5x + 4y = 20. 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?(103 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(81 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(15 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!(12 votes)

- is Y always = to 0?(15 votes)
- Y is always= 0 when the point is a X-intercept.

In case of a Y - intercept X is always equal to 0(2 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(9 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.(12 votes)

- What if you have a repeating decimal in your intercept? What can you do to avoid it?(8 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.(11 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?(8 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).(2 votes)

- if the x intercept is 2 and the y intercept is -1 what is the slope of the corresponding line?(5 votes)
- What is the importance of an x or y intercepts ?(6 votes)
- They show how much a line is shifted of the origin. If you didn't have intercepts,
**every**line would go through the origin. In real life though, most things have an intercept and don't go through the origin.(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)(2 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.(11 votes)

- how do you know if the intercept you found is right? And why do we have to put the answer as an irrational? and how do we know when to put it as an irrational?(2 votes)
- You can always plug in the point to see if it works in the equation. So with -5x+4y=20, you have an x intercept of (-4,0) and -5(-4)+4(0)=20 gives 20=20, so it is correct. With (0,5), -5(0)+4(5)=20 also gives 20=20, so they work.

I am not sure what you mean by having the answer as an irrational number in linear equations. Almost all linear equations will have rational solutions especially what you deal with in Algebra I. It is more likely to get irrational solutions when you are talking about quadratic equations.(4 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.