Answered

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13. The table shows the height of a plant as it grows. Which equation in point-slope form gives the
plant's height at any time?
Time (months)
Plant Height
(cm)
2
16
4
32
6
48
8
64
Oy - 16 = S(x - 2)
Oy - 16 = 3x - 2
3- 16 = S(x - 2)
The relationship is non-linear

Sagot :

Given:

Table of values.

To find:

The equation in point slope form.

Solution:

From the given table it is clear that, the relationship is linear because the rate of change is constant because if x-value increases by 2 then y-values increases by 16.

Consider any two points from the table, i.e., (2,16) and (4,32).

[tex]Slope=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

[tex]Slope=\dfrac{32-16}{4-2}[/tex]

[tex]Slope=\dfrac{16}{2}[/tex]

[tex]Slope=8[/tex]

The point is (2,16) and the slope is 8, so the point slope form is

[tex]y-y_1=m(x-x_1)[/tex]

[tex]y-16=8(x-2)[/tex]

Therefore, the relationship is linear and point slope form is [tex]y-16=8(x-2)[/tex].

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