Question

Which functions have a positive rate of change and which have a negative rate of change?

Answer 1

Column A
1.
2x – 3y = 9
2.
y = −4x + 5
3.
x y
−1 −5
1 1
3 7

4.
x y
1 −2
2 −6
3 −10

Answer 2

Column B
A.
positive
B.
negative

Answer 3

Do you have any way of graphing these?

Answer 4

nope sorry

Answer 5

Rate of change is also known as slope.

Answer 6

Okay then.. one sec.

Answer 7

2x – 3y = 9

To find the slope of this, change it into slope-intercept form(y = mx + b):

2x - 3y = 9

Subtract 2x to both sides:

-3y = -2x + 9

Divide -3 to both sides:

y = 2/3x + 3

Now it's in the form of y = mx + b, where m = slope. So here the slope or average rate of change is POSITIVE 2/3.

Answer 8

y = -4x + 5

Do you know what the slope is here? @RainbowBubbles01

Answer 9

hold on

Answer 10

It's already in the form of y = mx + b.

Answer 11

no i dont -_- i have been so busy this week i am so burnt out ,luckily today is friday

Answer 12

y = mx + b

m = slope

y = -4x + b

What's the slope? Hint: the number next to \(x\).

Answer 13

-4

Answer 14

Yep, and -4 is negative so y = -4x + 5 has a negative slope.

Answer 15

sooo....

Answer 16

Now for #3, we can take two points from the table and plug them into the slope formula.

Let's take (1, 1) and (3, 7):

\(m = \dfrac{y_2-y_1}{x_2-x_1}\)

\(m = \dfrac{7-1}{3-1}\)

Subtract:

\(m = \dfrac{6}{2}\)

Can you divide that? @RainbowBubbles01

Answer 17

yeah

Answer 18

wait divide 6/2?

Answer 19

Yes.

Answer 20

3

Answer 21

.

Answer 22

Yep, and that's positive.

So so far we have:

1 - Positive
2 - Negative
3 - Positive

Now we do the same thing with #4:

Let's take (2, -6) and (3, -10):

\(m = \dfrac{y_2-y_1}{x_2-x_1}\)

\(m = \dfrac{-10+6}{3-2}\)

Add & Subtract:

\(m = \dfrac{-4}{1}\)

Can you divide that? @RainbowBubbles01

Answer 23

-4

Answer 24

Yep, and that's negative so:

Question 1 - Positive
Question 2 - Negative
Question 3 - Positive
Question 4 - Negative

Answer 25

thank you thank you thank you, can you help with 4 more?

Answer 26

@iGreen

Answer 27

Sure, just close this one first and open a new one.