"y" varies directly as "x"

[S.Hobden]

Hello,
I was checking over my Daughters assignment and I dont know the answer to this question.

If "y" varies directly as "x", and if x = - 4.5 when y = 13.5, find "x" when y = 24

If you could help that'd be great!

 

[arthur ohlsten]

y=mx+b a straight line relationship [y varies directly with x]

eq.1____13.5=m[-4.5]+b
eq.2____ 24=mx+b

subtract eq1 from eq2
10.5=m[x+4.5] no unique solution
for instance y=24 when x=0 or
y=24 when x=3

There must have been other information your daughter missed, such as the slope of the line.
Arthur

 

[soroban]

Hello, S.Hobden!

If $\displaystyle y$ varies directly as $\displaystyle x$, and if $\displaystyle x\,=\,- 4.5$ when $\displaystyle y\,=\,13.5,\,$ find $\displaystyle x$ when $\displaystyle y\,=\,24$

Since $\displaystyle y$ varies directly as $\displaystyle x$,
$\displaystyle \;\;$the equation is: $\displaystyle \:y\:=\:kx\,\:$ for some constant $\displaystyle k$.

We are given: $\displaystyle \,x\,=\,-4.5,\;y\,=\,13.5$
Substitute: $\displaystyle \,13.5\:=\:k(-4.5)\;\;\Rightarrow\;\;k\,=\,-3$

Hence, the equation is: $\displaystyle \,y\;=\;-3x$

When $\displaystyle y\,=\,24$, we have: $\displaystyle \,24\:=\:-3x\;\;\Rightarrow\;\;x\,=\,-8$

 

[S.Hobden]

Thankyou very much for your help! Also, what you are doing is a wonderful help to my kids.

 

[Denis]

This (to me) is the EASIEST way:

-4.5    x
---- = --
13.5   24

Crisscross multiplication:
13.5x = -4.5(24)
13.5x = -108
x = -108 / 13.5 = -8

 

[arthur ohlsten]

The answer y=-3x is the answer to given:
y varies directly with x
when x=-4.5 y=13.5
when y=0 x=0
find y when x = 13.5

to see the general answer on a a xy graph
At x=-4.5 y= 13.5 make a dot
at y=24 draw a horizontal line
Any point on that line satisfys the given data , and gives a value of "b"=0 only at
the point x=-8 y=24

I might be misunderstanding the question, but the answer y=-3x is only 1 of a infinite number of possible answers
Arthur

 

[Denis]

Well Arthur, seems like this is a math question from a grade 6 or so student
(he's helping his kids), so I doubt that the answer is as involved as you show
(I'm not saying what you show is not proper!).

 

[arthur ohlsten]

S Hobden-
You are right if the student is a 6th grade student. But the father listed the problem as advanced algebra. If the student is a college student then the problem was probably given as a problem relative to a straight line definition.
I gave the general solution because I assumed a advanced high school, or freshman college student.
Arthur

 

[S.Hobden]

My Daughter is in Grade 10 (Math 10 pure)

 

[Mrspi]

Am I missing something??

It doesn't matter (I don't think!) whether a student is in 6th grade, 10th grade, or 15th grade.

If y varies directly as x, then x and y are related as follows:

y/x = k
or
y = kx

Yes, this is a "straight line" (is there ANY OTHER KIND of line??).
The slope is "k".
The y-intercept is 0.

Every direct variation relationship is one where the line representing the relation passes through the origin.

Let's not overcomplicate things.....I do not think that the problem as originally stated had any missing information.

 

[Denis]

PIpe down, MrsPI; no need to get an ulcer;
was only trying to be helpful;
had I known this was a 10th grader, I wudda kept ma trap shut :wink:

And if a 6th grader and a 15th grader should receive the same explanation,
that's another question...I sure think NOT; but that's my opinion.

 

[arthur ohlsten]

S.Hobden-
Sorry I didn't know your daughter was in 10th grade then the a:b :: c:d or a/b=c/d is probably what she was studying. Sorry for the answer "all straight lines passing through 13.5,-4.5 except for a vertical or horizontal line"

By the way there are many lines that are not "a straigt line". The circumference of a circle, a great circle on a sphere, etc.
I assume mrs.pi is a student, or one not that familiar with mathematics.

Again, sorry for the confusion, but at least your daughter learned that all adults don't always agree, and yet all are "correct"
Arthur

 

[S.Hobden]

Hey

No problem, We're just studying for her final.
So theres plenty of time to correct things!