|
Question 131728: The word problem is this:
Suzanne had 9 CDs. She decided to add CDs to her collection at the same rate each week. After 2 weeks, she had 15 CDs.In how many weeks did she have 27 CDs? How many CDs did she have after 8 weeks?
MY daughter plotted it out on a graph and came up with (0,9) (2,15) (6,27) and (8,33) Which would mean that she had 27 CDs in 6 weeks and 33 CDs in 8 weeks.
And then she was asked to write an equation for this word problem
Her answer was : Y= 9+2X
Could you please tell me if this is correct?
Thank You
Mother lost in Algebra
Found 2 solutions by josmiceli, solver91311:
Answer by josmiceli(19441)   (Show Source):
You can put this solution on YOUR website! You did pretty good
The assumption when you do a plot, the INdependant variable,
in this case, weeks, is plotted on the x-axis. The DEpendant
variable, in this case, CDs is plotted on the y-axis. That's
because the number of CDs DEpends on what week it is. You got
that right- I'm just clarifying.
The general form for the linear relation is 
where  is the slope and  is where the line crosses
the y-axis, in this case the CD axis. So, is saying
how many CDs do I have when the week is zero. I have 9, so
 . The slope, is defined as the change in
 divided by the change in  .
Read this as: (CDs after 2 wks - CDs when I start) / (2 wks - 0 wks)
So now I have the equation
----------------
x = 0
----------------
y = 27
----------------
x = 8
These are the points you got, but the equation was wrong
Good luck
Answer by solver91311(24713)  (Show Source):
You can put this solution on YOUR website! The only thing wrong is a slight mis-step on writing the equation. There are two ways to look at this, and both of them come up with the same result.
If you plot the two points you are given in the problem statement on a graph, namely (0,9) and (2,15), you can see that if you move 2 units in the horizontal direction, you have to move 6 units in the vertical direction. This corresponds to a slope of 3, because 6/2 = 3.
From the information on the graph, you can write the slope-intercept form of the equation directly by filling in m and b in the formula  , where m is the slope number and b is the y-intercept. The slope is the 3 we just calculated above and the y-intercept is the value of the y-coordinate at the point where the line intersects the y-axis. That point for this problem is (0,9), so the y-intercept, or b value is 9. That makes the equation  .
The other method is a straight algebraic approach using the two-point form of the line: Given  :( , ) and  :( , ), the equation representing the set of ordered pairs forming a line through and is given by:
For any specific problem, just plug in the numbers you are given. The selection of which point is 1 and which is 2 is completely arbitrary, so long as you remain consistent once you have made a choice. In this case let : (2,15) and : (0,9).
Do the arithmetic:
You now have an equation that is perfectly valid, but now it becomes a matter of form. Generally, you are either asked to put the equation into slope-intercept form as we discussed previously (), or standard form, ( ).
Distribute the 3:
Add 15 to both sides:
, and you have the slope intercept form.
From here, just add -3x to both sides:
 , and you have the standard form with a = -3, b = 1, and c = 9.
Hope that helps,
John
|
|
|
| |
