Finding the equation of a line through (-2, 1) and (2, 3)

[nukeman]

Homework Statement

Just doing some review, and I keep getting the wrong answer. Can someone explain this for me please?

The equation of the straight line through the points (-€2; 1) and (2; 3) is

Book says the correct answer is 2y = x + 4

What are the steps to get 2y = x + 4 ?

Homework Equations

The Attempt at a Solution

Here is what I did:

Slope = 1/2
so y =1/2x + c

taking 2 points, 2,3 as in x and y

3=1/2(2)+c
3=1/4+c

2.75=c

so y=1/2x + 2.75

Im so lost...:(

 

[Mark44]

Homework Statement

Just doing some review, and I keep getting the wrong answer. Can someone explain this for me please?

The equation of the straight line through the points (-€2; 1) and (2; 3) is

Book says the correct answer is 2y = x + 4

What are the steps to get 2y = x + 4 ?

Homework Equations

The Attempt at a Solution

Here is what I did:

Slope = 1/2
so y =1/2x + c

taking 2 points, 2,3 as in x and y

3=1/2(2)+c
3=1/4+c

(1/2)(2) = 1, not 1/4.

2.75=c

so y=1/2x + 2.75

Im so lost...:(

 

[nukeman]

Ahhhg, why did I put that! lol

Right, so:

I still don't quite udnerstand how the book got 2y = x + 4

 

[nukeman]

Ok here is what I got for finding an equation of a line thru these points: (-2,1) (2,3)

m = 1/2

so taking the points 2,3 I get the following:

3 = 1/2(2) + c

3 = 1 + c

2 = c

so, y = 1/2x + 2

But that's wrong...?

 

[SammyS]

Ok here is what I got for finding an equation of a line thru these points: (-2,1) (2,3)

m = 1/2

so taking the points 2,3 I get the following:

3 = 1/2(2) + c

3 = 1 + c

2 = c

so, y = 1/2x + 2

But that's wrong...?

It's clearer if you write it as

y = (1/2)x + 2 .​

That line does pass through points: (-2,1) and (2,3) .

 

[nukeman]

Then why does my book say this is the correct answer? 2y = x + 4

Is it because the book did not like the 1/2, so it multiplied it by 2 to get 1, and did same to all sides?

 

[SammyS]

...

Is it because the book did not like the 1/2, so it multiplied it by 2 to get 1, and did same to all sides?

Yes .

 

[soothsayer]

2y = x + 4 and y = 1/2 + 2 are the exact same things. The first way is just a little easier to write.

Easiest way to go about these problems for me is a system of equations.

y = mx + b
plug in conditions:
(1) 1 = -2x + b
(2) 3 = 2m + b

By adding (1) and (2), we obtain 4 = 2b, so b = 2

Plug b = 2 into (2) (we could have picked either equation), we get 1 = 2m, so m = 1/2

plugging back into the original formula, we get y = (1/2)x + 2, or 2y = x + 4, both are correct.

 

[Mark44]

2y = x + 4 and y = 1/2 + 2 are the exact same things.

No, 2y = x + 4 and y = (1/2)x+ 2 are the same. (Technically, they are equivalent equations.)

The first way is just a little easier to write.

Easiest way to go about these problems for me is a system of equations.

y = mx + b
plug in conditions:
(1) 1 = -2x + b
(2) 3 = 2m + b

By adding (1) and (2), we obtain 4 = 2b, so b = 2

Plug b = 2 into (2) (we could have picked either equation), we get 1 = 2m, so m = 1/2

plugging back into the original formula, we get y = (1/2)x + 2, or 2y = x + 4, both are correct.