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Answers for number 7,8,9??

Answers for number 7,8,9??-example-1

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The linear functions are:

7. f(x) = 0.2x

8. g(x) = 3x + 5

9. h(x) = -2x - 2

Representing the linear functions for the given data using function notation:

7. (x, y)

Given data points: (-3, -0.6), (1, 0.2), (7, 1.4)

Calculate the slope (m):

m = change in y / change in x

m = (0.2 - (-0.6)) / (1 - (-3) = 0.8 / 4 = 0.2

Choose one point to find the y-intercept (b).

Use (1, 0.2):

y = mx + b

0.2 = 0.2(1) + b

0.2 = 0.2 + b

b = 0

So, the linear function is: f(x) = 0.2x

8. (x, y)

Given data points: (-5, -10), (-2, -1), (4, 17)

Calculate the slope (m):

m = change in y / change in x

m = (-1 - (-10)) / (-2 - (-5)) = 9 / 3 = 3

Choose one point to find the y-intercept (b).

Use (-2, -1):

y = mx + b

-1 = 3(-2) + b

-1 = -6 + b

b = 5

So, the linear function is: g(x) = 3x + 5

9. (x, y)

Given data points: (-5, 8), (-2, 2), (8, -18)

Calculate the slope (m):

m = change in y / change in x

m = (2 - 8) / (-2 - (-5)) = -6 / 3 = -2

Choose one point to find the y-intercept (b).

Use (-2, 2):

y = mx + b

2 = -2(-2) + b

2 = 4 + b

b = -2

So, the linear function is: h(x) = -2x - 2

Therefore, the linear functions are:

7. f(x) = 0.2x

8. g(x) = 3x + 5

9. h(x) = -2x - 2

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