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