Discover answers to your questions with Westonci.ca, the leading Q&A platform that connects you with knowledgeable experts. Ask your questions and receive precise answers from experienced professionals across different disciplines. Explore comprehensive solutions to your questions from knowledgeable professionals across various fields on our platform.
Sagot :
Building linear equations for f and g, it is found that the y-intercept of (f - g)(x) is of y = 8.
------------
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
Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. We're glad you visited Westonci.ca. Return anytime for updated answers from our knowledgeable team.
