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### Course: Functions 229-236>Unit 1

Lesson 3: 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)
• at where did 0 come from?
• 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.
• 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
• I'm confused at how he got 7/3 is equal to 6/3 + 1/3 ?
(1 vote)
• i understood nothing in the video
• I can explain!

The x-intercept of a line is the point at which the line crosses the x-axis.

In other words, it’s the value of x when y equals zero in the equation of the line.

For a line represented by the equation y=mx+b,
where m is the slope and b is the y-intercept, the x-intercept can be found by setting y to zero and solving for x.

So, if we set y to zero, we get:

0=mx+b

Solving for x gives us:

x=−b/m

This value of x is the x-intercept of the line. It represents the point on the x-axis where the line intersects. If the line never crosses the x-axis, then it has no x-intercept.

For example, the line

y=2x+3

has an x-intercept at x=−3/2
or x=−1.5.

This means the line crosses the x-axis at the point (-1.5, 0).

I hope this explanation helps! Let me know if you have any other questions.