Question

ONE QUESTION! @=people

Answer 1

@Michele_Laino

Answer 2

here we have to conjecture a linear relationship between y and x, namely:
y=a*x+b
x= elongation
y= applied mass

Answer 3

using your data, we can write:
\[\left\{ \begin{gathered}
70 = a \times 18 + b \hfill \\
100 = a \times 24 + b \hfill \\
\end{gathered} \right.\]

Answer 4

we have to solve that system for "a" and "b"

Answer 5

alright, solving for a and b

Answer 6

yes!

Answer 7

for example I solve the first equation for b, and I get:
\[b = 70 - 18a\]

Answer 8

then I substitute that expression into the second equation, so I can write:
\[100 = 24a + \left( {70 - 18a} \right)\]

Answer 9

what is a?

Answer 10

actualy no

Answer 11

we have to simplify as below:
\[100 = 24a + 70 - 18a\]

Answer 12

ok one sec

Answer 13

5

Answer 14

\[\begin{gathered}
100 = 70 + 6a \\
100 - 70 = 6a \\
\end{gathered} \]

Answer 15

ok one sec

Answer 16

ok! a= 5

Answer 17

a=5 for both

Answer 18

now I substitute a=5 into the first equation, for example, so I get:
\[\begin{gathered}
70 = 18 \times 5 + b \\
70 = 90 + b \\
\end{gathered} \]

Answer 19

what is b?

Answer 20

-20

Answer 21

ok! so our relationship is:
y=5x-20

Answer 22

you mean 1/5x

Answer 23

ohh I see nvm sorry

Answer 24

no, y= 5x-20
I have made an error, when I wrote:
x= elongation y= applied mass

Answer 25

nevertheless to get the right answer it is suffice to change x, y each other

Answer 26

so we can write:
x=5y-20

Answer 27

then we can solve that equality for y, and we get this result:
\[y = \frac{1}{5}x + 4\]

Answer 28

since your problem consider x as the applied weight
and y the elongation produced by that weight

Answer 29

as you can see I have conjectured viceversa

Answer 30

yes I get it

Answer 31

so, what is the right option?

Answer 32

D?

Answer 33

yes!