Question

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

Answer 1

`\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.