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

Column A                      Column B

1.____ 2x + 3y = −9       A.Positive

B.Negative

2._______ y = 3x − 6


3.______

x y

−1 9

0 7

1 5


4.______

x y

2 −8

3 −7

4 −6

Verified Answer :

iGreen

\(\sf2x+3y=-9\)

Convert to slope-intercept form, y = mx + b.

\(\sf2x+3y=-9\)

Subtract 2x to both sides:

\(\sf3y=-2x-9\)

Divide 3 to both sides:

\(\sf~y=-\dfrac{2}{3}x-3\)

Now it's in slope intercept form, y = mx + b where 'm' is the slope. So the slope here is -2/3, which is Negative.

\(\sf~y=3x-6\)

This is already in slope intercept form. So the slope here is 3, which is Positive.

For #3 and #4, take any two points from the table and plug them into the slope formula.

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

Let's take (0, 7) and (1, 5).
               x1 y1       x2 y2

\(\sf~m=\dfrac{5-7}{1-0}\)

Subtract:

\(\sf~m=\dfrac{-2}{1}\)

Divide:

\(\sf~m=-2\)

So the slope is negative.

For #4, let's take (2, -8) and (3, -7)
                         x1  y1       x2  y2

\(\sf~m=\dfrac{-7-(-8)}{3-2}\)

Subtract:

\(\sf~m=\dfrac{1}{1}\)

Divide:

\(\sf~m=1\)

So the slope is positive.

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