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### Course: Integrated math 1>Unit 4

Lesson 4: x-intercepts and y-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?
• 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.
y=5/-2+b. to find b, you just put in the y intercept. the equation is
y=5/-2+5
• is Y always = to 0?
• Y is always = 0 to find X-intercepts.
X is always =0 to find Y-intercepts.
• 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
• `-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!
• 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
• 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.
• What if you have a repeating decimal in your intercept? What can you do to avoid it?
• 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.
• 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?
• 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).
• 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)
• 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.
• if the x intercept is 2 and the y intercept is -1 what is the slope of the corresponding line?