Question

What is the prediction for the outcome when the independent variable is 2? (Round the answer to the nearest hundredth.)



A.
2.50

B.
30.00

C.
1.60

D.
24.00

Answer 1

@AllTehMaffs could you help me with this one too?

Answer 2

@AllTehMaffs

Answer 3

This looks like the same problem as the one you posted before....

Answer 4

And based on the question and the information given, it looks like the question might be asking you to find the equation of the line. Have you done problems where you have something that looks like

y = mx + b

?

Answer 5

yeah i have but i always get them wrong

Answer 6

Well then we'll get this one right ^_^

So in the equation

y = mx + b

Sp first, b, the y-intercept, is where the line hits the y-axis - Where does this line his the y-axis?

Answer 7

12???...

Answer 8

We're looking at the graph that has annual rainfall vs average growth rate this time, correct?

Answer 9

yes

Answer 10

K k. Then if you look at the line, where it hits the y-axis is where the line starts at the far left of the picture. It starts at the origin, so the line hits the y-axis at what value? (It's the second number in the ordered pair at the bottom left)

Answer 11

i dont know!! gah~ um im gonna say 0?

Answer 12

Correct!!! ^_^

Answer 13

YAY

Answer 14

Soooo, what next?

Answer 15

@AllTehMaffs ?

Answer 16

Sorry, had a phone call.

So then in the equation

y = mx + b

m is the slope. It's basically the steepness of the line. To find it, you have to find "the rise over the run" or
\[m= \frac{\text{how high the line goes up the y axis}}{\text{how far the line goes along the x axis}}=\frac{y_2 - y_1}{x_2-x_2}\]

and since the line starts at the origin, (0,0) we know that
\[y_1 = 0\]
and
\[x_1 = 0\]

Then y2 and x2 are the values of the ordered pair in the middle of the graph! Which are?

Answer 17

@AllTehMaffs we never finished this question lol, could you help me?

Answer 18

Fo sho. Can you come up with an equation for that line?

Answer 19

Fo sho. Can you come up with an equation for that line?

Answer 20

3,0? is that an equation lol

Answer 21

^_^ nope nope. An equation would be like the one in that last problem,
\[y=mx+b\]
so you find the slope with the ordered pairs, and then b is where the line crosses the y-axis

Answer 22

okay so i have to do this y1-x1 and y2-x2 first right?

Answer 23

the ys and xs are together, so
\[m = \frac{y_2-y_1}{x_2-x_1}\]
the rise over the run

Answer 24

but yah, you can find the slope first

Answer 25

wait i messed up...now im lost

Answer 26

You just subtracted each term in each pair - it's always one from each. x1 and y1 are both zero, so what would that give you if y2 and x2 are the pair on the right?

Answer 27

-3?

Answer 28

ordered pairs are of the form (x, y), and the slope is
\[m = \frac{y_2-y_1}{x_2-x_1}\]
And we know in this problem the first pair is (0, 0), so x1 = 0 and y1 = 0, leaving us with
\[m = \frac{y_2-0}{x_2-0}\]

Answer 29

is it 15-12 or 12-15?

Answer 30

you're going to be dividing 12 by 15

Answer 31

so its 0.8

Answer 32

yup yup. Then next, at what value does the line hit the y-axis?

Answer 33

12?

Answer 34

That's a point on the line. Where the line is farthest left is what you're looking for. It's also the y value of the first ordered pair in this problem.

Answer 35

0?

Answer 36

yup yup yup. so b=0, and we know that m=.8 , so plugging all of that into the form for an equation of a line
\[y = mx+b\]
gives you the equation of that line. What the problem is asking for is the predicted outcome (the y value) when the independent variable (x) is 2. So you plug in your x and find out what it gives for y.

Answer 37

what is x? so far its y=8x+0 right?

Answer 38

yeah. When you plug in a value for x its spits out a value for y, and when you plot those points on the graph it gives you your line. We want to look at one specific part of that, when the independent variable - x - is 2, so when x=2.

Answer 39

errr, make sure it's
\[y=.8x\]
but methinks that was just a typo ^_^

Answer 40

so .8*2 is 1.6? and that would be C?

Answer 41

Correct!

Answer 42

THANKS SO MUCH!!

Answer 43

good work

Answer 44

Very welcome. Happy mathing!