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### Course: Algebra 1 > Unit 4

Lesson 4: x-intercepts and y-intercepts# x-intercept of a line

Sal determines the x-intercept of a linear equation from a graph. Afterwards, he checks his work by plugging values back into the equation. Created by Sal Khan.

## Want to join the conversation?

- How do you find the y intercept?(18 votes)
- You can take the function f(x) = something (your funtion) so like f(x)=2x. you can input x=0 and find the output which would be the y intercept. So, lets actually have f(x) = 5x + 2. You input 0 for x and you get f(x) = 2. That is your y intercept(20 votes)

- How do you know where to put your intercepts when answering the problems.? I haven't been able to get 100% on the practice problems, because my answers need to be reversed, but I can't figure out where to place them.(11 votes)
- in slope-intercept form, ( y=mx+b ) b represents your y-intercept.(4 votes)

- for example how would you find the x intercept for a problem like this ?Y = x2 + 5x + 4

y = x squared plus five x plus four(5 votes)- It's a quadratic equation, which means it's a non-linear (is parabolic in shape). You can find the x-intercepts (usually there are 2, but there can be 1 or none) by completing the square, factoring or by using the quadratic formula. Which method I use depends on which one I think will make solving the problem easier. The easiest way to solve is to factor the quadratic equation.

x^2+5x+4=0

We set it equal to zero because we are looking for the x intercepts.

When y is 0 where will the parabola cross the x-axis

To solve by factoring we ask ourselves: What two numbers add up to the middle term and are the product of the last term?

4*1=4 (last term)

4+1=5 (middle term)

(x+4) (x+1)

set them both equal to zero to find the x intercept

x+4=0

subtract 4 from both sides

x=-4

x+1=0

subtract 1 from both sides

x=-1

x intercepts are -4 and -1. Or the points where the parabola crosses the x-axis are (-4,0) and (-1,0).(10 votes)

- Can't you find the intercept by doing -b/2a, or is that finding the vertex?(5 votes)
- A vertex is a corner, where two lines meet. A straight line by itself doesn't have a vertex.

The easiest way to find the x intercept is to figure out what value x will have when y = 0.

So if you have an equation of a line: 2y + 4x = 28

you substitue "0" in for your y and solve:

2 (0) + 4x = 28

4x = 28

x = 7

The x intercept is (7,0)(8 votes)

- Slope intercept form is y=mx+b.

Is there a way to use the x-intercept instead of the y-intercept. Use p for the y-intercept in your equation.

My attempt:

y = mx + b

0 = mx + b

0 = x + b/m

x = -b/m

let p be the x-intercept

therefore: p = -b/m

Therefore:y = mx - mp

Am I right?(5 votes)- If m = 3 and b = 2 (Substitute) 0 = 3x + 2 (0 = mx + b) (Subtract b from both sides)

0-2 = 3x (y-b = mx) -2 = 3x (y-b = mx) (divide both sides by the amount x is multiplied by) -2/3 = x(5 votes)

- at0:48where did 0 come from?(6 votes)
- We need to find the x intercept. So, as it is a point on the x axis, the y coordinate has to be 0. So, we substitute y = 0 into the equation.(3 votes)

- i understood nothing in the video(6 votes)
- How would I find the x and y intercepts and graph them if I have a function 3x - 5y=15(5 votes)
- You can substitute the x or y to find the other intercept or vice versa. For example, if x was zero in 3x - 5y = 15 then your y-intercept is -3. Or for example, if y was zero in 3x - 5y = 15 then your y-intercept is 5.(1 vote)

- Theoretically could there be a "z" axis?

Like on a 3 dimensional graph?

Do those exist?(3 votes)- Yes, we could have a z-axis. You could graph planes, spheres, and all sorts of other figures. You probably won’t run into 3D graphs unless you do higher-level math. Here is an article on 3D space from the multivariable calculus course: https://www.khanacademy.org/math/multivariable-calculus/thinking-about-multivariable-function/ways-to-represent-multivariable-functions/a/multidimensional-graphs

You probably won’t understand all of it yet, but you might find it interesting!(3 votes)

- I have a question what is the equation of x intercept?(3 votes)
- There is no equation. You take the linear equation that you have and you replace Y with 0. Then, solve for X. You will have a point on the line at (x-value, 0) where the x-value is the value you found. This point is where the line cross the x-axis (so, it is the x-intercept).(2 votes)

## Video transcript

The graph of the line
2y plus 3x equals 7 is given right over here. Determine its x-intercept. The x-intercept is the x
value when y is equal to 0, or it's the x value
where our graph actually intersects the x-axis. Notice right over here
our y value is exactly 0. We're sitting on the x-axis. So let's think about what
this x value must be. Well, just trying to
eyeball a little bit, it's a little over 2. It's between 2 and 3. It looks like it's
less than 2 and 1/2. But we don't know
the exact value. So let's go turn to the equation
to figure out the exact value. We essentially
have to figure out what x value, when
y is equal to 0, will have this equation be true. So we could just say 2 times
0 plus 3x is equal to 7. Well, 2 times 0 is
just going to be 0, so we have 3x is equal to 7. Then we can divide both
sides by 3 to solve for x, and we get x is equal to 7/3. Does that look like 7/3? Well, we just have
to remind ourselves that 7/3 is the same
thing as 6/3 plus 1/3. And 6/3 is 2. So this is the same
thing as 2 and 1/3. Another way you could
think about it is 3 goes into 7 two times, and
then you have a remainder of 1. So you've still got
to divide that 1 by 3. It's 2 full times
and then a 1/3, so this looks like 2 and 1/3. And so that's its
x-intercept, 7/3. If I was doing this on the
exercise on Khan Academy, it's always a little easier to
type in the improper fraction, so I would put in 7/3.