At Westonci.ca, we connect you with the best answers from a community of experienced and knowledgeable individuals. Get accurate and detailed answers to your questions from a dedicated community of experts on our Q&A platform. Our platform provides a seamless experience for finding reliable answers from a network of experienced professionals.
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
Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. Your questions are important to us at Westonci.ca. Visit again for expert answers and reliable information.
