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anonymous

  • one year ago

I don't just want the answer... I want help on how to figure this out... I don't understand it pleasssseeee I will give medals The table below represents a linear function f(x) and the equation represents a function g(x): x f(x) −1 −9 0 −1 1 7 g(x) g(x) = 3x − 2 Part A: Write a sentence to compare the slope of the two functions and show the steps you used to determine the slope of f(x) and g(x).

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  1. mathstudent55
    • one year ago
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    The slope of the line that passes through points \((x_1, y_1)\) and \((x_2, y_2)\) is \(m = \dfrac{y_2 - y_1}{x_2 - x_1} \)

  2. mathstudent55
    • one year ago
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    When the equation of a line is written in the slope-intercept form, \(y = mx + b\), m is the slope, and b is the y-coordinate of the y-intercept.

  3. anonymous
    • one year ago
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    right i have that so far -1 -(-9) over 0-(-1) =8

  4. mathstudent55
    • one year ago
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    To find the slope of function f(x), choose any to points from that function. I see that you are using the points (-1, -9) and (0, -1). \(m = \dfrac{-1 - (-9)}{0 - (-1)} = \dfrac{8}{1} = 8\) You are correct. the slope of function f(x) is 8. Now notice that function g(x) is written in the slope-intercept form, so you can read the slope right off the equation. What is the slope of the function g(x)?

  5. anonymous
    • one year ago
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    3

  6. mathstudent55
    • one year ago
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    Correct. The slope of f(x) is 8, and the slope of g(x) is 3. That takes care of part A.

  7. anonymous
    • one year ago
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    ok wait

  8. anonymous
    • one year ago
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    I guess im confused they want a sentence how would i write that or am i reading into it to much :(

  9. mathstudent55
    • one year ago
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    I can tell you what to write, but it's already written above. Use your own calculation of the slope to show how you found the slope of f(x). Then state that the slope of g(x) is 3 because g(x) is written in the slope-intercept form, which allows you to read the slope right off the equation.

  10. anonymous
    • one year ago
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    oh ok sorry

  11. anonymous
    • one year ago
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    so for part b f(x) is steeper/Bigger than G(x) because the slope of F(x) is 8 and the slope of G(x) is only 3 ... is this correct

  12. anonymous
    • one year ago
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    @mathstudent55

  13. mathstudent55
    • one year ago
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    Part A dealt with the slopes. Part B deals with the y-intercepts, not slopes.

  14. mathstudent55
    • one year ago
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    The y-intercept is the point where the line crosses the y-axis. It is b in the slope-intercept equation of a line.

  15. mathstudent55
    • one year ago
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    We know b for the g(x). It is -2 for g(x). Now we need to find b for f(x).

  16. mathstudent55
    • one year ago
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    Let's find the slope-intercept form of the equation of f(x) y = mx + b For f(x), we know m = 8 since we calculated it in part A. We have: y = 8x + b

  17. mathstudent55
    • one year ago
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    We need to find b. We can use any point in f(x) to find b. Let's use point (0, -1) y = 8x + b -1 = 8(0) + b -1 = b b = -1 That means the equation of f(x) is: f(x) = 8x - 1

  18. mathstudent55
    • one year ago
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    Now we see the y-intercept of f(x) is -1, and the y-intercept of g(x) is -2. Now we can compare them.

  19. anonymous
    • one year ago
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    ohh so F(x) is bigger because it is -1 and G9x) is -2

  20. anonymous
    • one year ago
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    that should say G(x) is -2

  21. anonymous
    • one year ago
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    @mathstudent55

  22. mathstudent55
    • one year ago
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    You are correct. You mean to say: The y-intercept of function f(x) is greater than the y-intercept of function g(x) because -1 is greater than -2.

  23. anonymous
    • one year ago
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    awesome thank you

  24. mathstudent55
    • one year ago
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    yw

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