Question 1

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?

Accepted Answer

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

Question 2

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

Accepted Answer

`-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!

Question 3

is Y always = to 0?

Accepted Answer

Y is always= 0  when the point is a X-intercept.
In case of a Y - intercept X is always equal to 0

Question 4

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

Accepted Answer

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.

Question 5

What if you have a repeating decimal in your intercept? What can you do to avoid it?

Accepted Answer

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.

Question 6

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?

Accepted Answer

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).

Question 7

What is the importance of an x or y intercepts  ?

Accepted Answer

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.

Question 8

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)

Accepted Answer

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.

Question 9

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?

Accepted Answer

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.

Algebra 1

Course: Algebra 1 > Unit 4

Intercepts from an equation

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