Respuesta :
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:
[tex]y = mx + b[/tex]
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 change in y divided by change in x, thus:
[tex]m = \frac{14 - 20}{-4 - (-6)} = -\frac{6}{2} = -3[/tex]
Then
[tex]f(x) = -3x + b[/tex]
Point (-6, 20) means that when [tex]x = -6, y = 20[/tex], and this is used to find b.
[tex]20 = -3(-6) + b[/tex]
[tex]18 + b = 20[/tex]
[tex]b = 2[/tex]
Thus
[tex]f(x) = -3x + 2[/tex]
- Now, function g has two points, (-6, -36) and (-4, -26), and the slope is:
[tex]m = \frac{-26 - (-36)}{-4 - (-6)} = \frac{10}{2} = 5[/tex]
Then
[tex]g(x) = 5x + b[/tex]
Applying point (-6, -36):
[tex]-36 = 5(-6) + b[/tex]
[tex]b = -6[/tex]
Then
[tex]g(x) = 5x - 6[/tex]
The subtraction (f - g)(x) is:
[tex](f - g)(x) = f(x) - g(x) = -3x + 2 - 5x + 6 = -8x + 8[/tex]
Thus the y-intercept is y = 8.
A similar problem is given at https://brainly.com/question/16302622
