several problems

B

Belby

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Sep 2, 2009
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I am stuck again! I need help on a few problems. The first one:
If the equation of the line through the points (3,4) and (-1,7) is written as y=A+B(x+1) then, A=? and B=?. First I found the slope w/Y2-Y1/X2-X1, m=-3/4. Then I worked the slope intercept form y=mx+b and rec'd 6.25 for my answer. Then I also worked with point slope form. I am lost. Help! Everything I entered on mathclass.org has been wrong. I just need help.
 
Belby said:
I am stuck again! I need help on a few problems. The first one:
If the equation of the line through the points (3,4) and (-1,7) is written as y=A+B(x+1) then, A=? and B=?. First I found the slope w/Y2-Y1/X2-X1, m=-3/4 correct. Then I worked the slope intercept form y=mx+b and rec'd 6.25 for my answer --> for what?. Then I also worked with point slope form. I am lost. Help! Everything I entered on mathclass.org has been wrong. I just need help.
Click to expand...

y=A+B(x+1)

y = A + Bx + B = Bx + (A+B)

slope = B = -0.75

intercept = (A+B) = 6.25

then

A = 6.25 + .75 = 7

Are these the answers you got?
 
yes. I got both those answers. Is this correct? A is 3/4 and b is 6.25.
 
Belby said:
… If … y = A + B(x + 1) then, A=? and B=? … This tells us that we're looking for two numbers.

… rec'd 6.25 for my answer … This is your answer for what ?

… Everything I entered on mathclass.org has been wrong … I do not know what this means. Is it important, for this exercise ?
Click to expand...


Let's start by writing the equation of the line that passes through the two given points.

You correctly determined the slope; it's m = -3/4.

There are different approaches for the next step; I'm going to use the Point-Slope Formula with the coordinates (3,4) as (x1,y1).

y - y1 = m(x - x1)

y - 4 = -3/4(x - 3)

This works out as:

y = -(3/4)x + 25/4

Now that we have the equation, we need to rearrange it into the form given in the exercise:

y = A + B(x + 1)

Let's expand the righthand side of this:

A + Bx + B

Now, we need to think symbolically. How can we write A + Bx + B so that it matches the form -(3/4)x + 25/4 ?

Here's how: Bx + (A + B)

Do you see it ? 8-)

In other words, the term Bx corresponds to the term -(3/4)x.

The expression (A + B) corresponds to 25/4.

Therefore, we have B = -3/4 and A + B = 25/4.

Substitute the value for B into A + B = 25/4.

A - 3/4 = 25/4

Finish by adding 3/4 to both sides of this latest equation, to find that A = 28/4 (which is 7).

A = 7 and B = -3/4

Let's check this result !

y = A + B(x + 1)

y = 7 - 3/4(x + 1)

y = 7 - (3/4)x - 3/4

y = -(3/4)x + 7 - 3/4

y = -(3/4)x + 28/4 - 3/4

y = -(3/4)x + 25/4

That's our line !

The answer checks.

Cheers ~ Mark

 
Belby said:
yes. I got both those answers. Is this correct? A is 3/4 and b is 6.25.
Click to expand...

I don't think I said that.

Read your original problem - very carefully.

What is it that asking you to find (NOT the slope or intercept)?

Then - read my answer very carefully.

What did I highlight (NOT the slope or intercept)?
 
If the equation of the line through the points (3,4) and (-1,7) is written as y=A+B(x+1) then, A=? and B=?. First I found the slope w/Y2-Y1/X2-X1, m=-3/4. Then I worked the slope intercept form y=mx+b and rec'd 6.25 for my answer. Then I also worked with point slope form. I am lost. Help! Everything I entered on mathclass.org has been wrong. I just need help.
Click to expand...

Here are some other thoughts.

You’re off to a good start (but in a roundabout direction); you correctly found the slope-intercept equation is

y = (-3/4)x + 6.25

We want to change x to (x + 1), but whatever we add to one side of the equation, we must also add to the other:

y + ? = (-3/4)(x + 1) + 6.25

How much has been added to the right side? Since there is a coefficient of (-3/4) out front, we’ve actually added (-3/4)(1) = -3/4 to the right hand side. So the equation becomes

y + (-3/4) = (-3/4)(x + 1) + 6.25

Rearranging, we get

y = (-3/4)(x + 1) + 6.25+ 3/4 = (-3/4)(x + 1) + 7
A = 7
B = -3/4

***
Let’s consider a more direct approach. This problem is looking for some “new” form, and you’ve been given the points (3,4) and (-1,7) and that

y = A + B(x + 1)

Just substitute the two known points into this form to create two equations:

4 = A + B(3 + 1)
7 = A + B(-1 + 1)

You now have a system of equations with two equations and two unknowns. Can you solve for A and B from here? Simplifying and combining (by subtracting the second equation from the first), we get

-3 = 4B
B = -3/4

Substituting back into the first equation,

4 = A + (-3/4)(3 + 1)
4 = A – 3
A = 7

Voila!
 


Belby: Are you thinking that B and b mean the same thing?

They don't.

B and b are two different numbers.

In other words, B is not the y-intercept.

 
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