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## Algebra I (2018 edition)

### Course: Algebra I (2018 edition)>Unit 5

Lesson 2: 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?
• 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
• 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.
• in slope-intercept form, ( y=mx+b ) b represents your y-intercept.
• 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
• 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).
• Can't you find the intercept by doing -b/2a, or is that finding the vertex?
• 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)
• 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?
• 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
• How would I find the x and y intercepts and graph them if I have a function 3x - 5y=15
• 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?
• I have a question what is the equation of x intercept?
• 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).
• What is a slope?