Building linear equations for f and g, it is found that the y-intercept of (f - g)(x) is of y = 8.
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A linear function has the following format:
![y = mx + b](https://tex.z-dn.net/?f=y%20%3D%20mx%20%2B%20b)
In which:
- m is the slope, which is the rate of change.
- b is the y-intercept, which is the value of y when x = 0.
- Function f has two points, (-6,20) and (-4,14).
- The slope is given by <u>change in y divided by change in x</u>, thus:
![m = \frac{14 - 20}{-4 - (-6)} = -\frac{6}{2} = -3](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7B14%20-%2020%7D%7B-4%20-%20%28-6%29%7D%20%3D%20-%5Cfrac%7B6%7D%7B2%7D%20%3D%20-3)
Then
![f(x) = -3x + b](https://tex.z-dn.net/?f=f%28x%29%20%3D%20-3x%20%2B%20b)
Point (-6, 20) means that when
, and this is used to find b.
![20 = -3(-6) + b](https://tex.z-dn.net/?f=20%20%3D%20-3%28-6%29%20%2B%20b)
![18 + b = 20](https://tex.z-dn.net/?f=18%20%2B%20b%20%3D%2020)
![b = 2](https://tex.z-dn.net/?f=b%20%3D%202)
Thus
![f(x) = -3x + 2](https://tex.z-dn.net/?f=f%28x%29%20%3D%20-3x%20%2B%202)
- Now, function g has two points, (-6, -36) and (-4, -26), and the slope is:
![m = \frac{-26 - (-36)}{-4 - (-6)} = \frac{10}{2} = 5](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7B-26%20-%20%28-36%29%7D%7B-4%20-%20%28-6%29%7D%20%3D%20%5Cfrac%7B10%7D%7B2%7D%20%3D%205)
Then
![g(x) = 5x + b](https://tex.z-dn.net/?f=g%28x%29%20%3D%205x%20%2B%20b)
Applying point (-6, -36):
![-36 = 5(-6) + b](https://tex.z-dn.net/?f=-36%20%3D%205%28-6%29%20%2B%20b)
![b = -6](https://tex.z-dn.net/?f=b%20%3D%20-6)
Then
![g(x) = 5x - 6](https://tex.z-dn.net/?f=g%28x%29%20%3D%205x%20-%206)
The subtraction (f - g)(x) is:
![(f - g)(x) = f(x) - g(x) = -3x + 2 - 5x + 6 = -8x + 8](https://tex.z-dn.net/?f=%28f%20-%20g%29%28x%29%20%3D%20f%28x%29%20-%20g%28x%29%20%3D%20-3x%20%2B%202%20-%205x%20%2B%206%20%3D%20-8x%20%2B%208)
Thus the y-intercept is y = 8.
A similar problem is given at brainly.com/question/16302622