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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

Sagot :

iGreen
[tex]\sf2x+3y=-9[/tex]

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

[tex]\sf2x+3y=-9[/tex]

Subtract 2x to both sides:

[tex]\sf3y=-2x-9[/tex]

Divide 3 to both sides:

[tex]\sf~y=-\dfrac{2}{3}x-3[/tex]

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.

[tex]\sf~y=3x-6[/tex]

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.

[tex]\sf~m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

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

[tex]\sf~m=\dfrac{5-7}{1-0}[/tex]

Subtract:

[tex]\sf~m=\dfrac{-2}{1}[/tex]

Divide:

[tex]\sf~m=-2[/tex]

So the slope is negative.

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

[tex]\sf~m=\dfrac{-7-(-8)}{3-2}[/tex]

Subtract:

[tex]\sf~m=\dfrac{1}{1}[/tex]

Divide:

[tex]\sf~m=1[/tex]

So the slope is positive.
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