Help Meh PleAse: Fill in the blanks 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

Answers

Answer 1
Answer: \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=-(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=(y_2-y_1)/(x_2-x_1)

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

\sf~m=(5-7)/(1-0)

Subtract:

\sf~m=(-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=(-7-(-8))/(3-2)

Subtract:

\sf~m=(1)/(1)

Divide:

\sf~m=1

So the slope is positive.

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