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anonymous

  • one year ago

which function has the largest slope? 1) x f(x) -3 -10 -1 -7 1 -4 2) g(x) equals one-half x plus 3 3) Lance gains 1 level each time he plays his favorite video game. He started at level 10

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  1. mathstudent55
    • one year ago
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    For 1), you have 3 points of the function. Use any two points and find the slope. For points \((x_1, y_1) \) and \((x_2, y_2) \), the slope is \(slope = m = \dfrac{y_2 - y_1}{x_2 - x_1} \)

  2. anonymous
    • one year ago
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    i dont know how to do any of this /:

  3. mathstudent55
    • one year ago
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    What do you get for the slope in 1)?

  4. mathstudent55
    • one year ago
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    Ok. For part 1), let's choose the points (-3, -10) and (1, -4). Each point has an x-coordinate followed by a y-coordinate like this: (x, y)

  5. mathstudent55
    • one year ago
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    To find the slope, find the difference of the y-coordinates and divide by the difference of the x-coordinates.

  6. mathstudent55
    • one year ago
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    For those two points, what are the y-coordinates?

  7. anonymous
    • one year ago
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    2/-3 ?

  8. mathstudent55
    • one year ago
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    The y-coordinates are -10 and -4 The x-coordinates are -3, 1 Subtract the y-coordinates and divide by the subtraction of the x-coordinates to get the slope. \(slope = m = \dfrac{-10 - (-4)}{-3 - 1} = \dfrac{-6}{-4} = \dfrac{3}{2} \)

  9. vera_ewing
    • one year ago
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    Great explanation @mathstudent55 ! It's very helpful! :)

  10. mathstudent55
    • one year ago
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    Now we need to find the slope for part 2).

  11. mathstudent55
    • one year ago
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    In part 2) we have an equation: \(g(x) = \dfrac{1}{2}x + 3\) This is the equartion of a line is slope-intercept form, \(y = mx + b\)m, where m = slope. We can read the slope directly. It is the number that multiplies x. For part 2_, the slope is \(\dfrac{1}{2} \).

  12. anonymous
    • one year ago
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    thank you so much

  13. mathstudent55
    • one year ago
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    Now we need to deal with part 3). Lance started at Level 10, so we start with y = 10 For each time, x, he plays, he gains 1 level, y. That means as x goes up 1, y goes up 1, and so on. We simply add x to 10, or \(y = x + 10\) Since this is also in slope-intercept form, we again read off the slope directly. Since x = 1x, the slope is 1.

  14. mathstudent55
    • one year ago
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    Now we have the 3 slopes, and you can decide which one is largest.

  15. anonymous
    • one year ago
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    so the first one is largest right?

  16. anonymous
    • one year ago
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    thank you!!

  17. mathstudent55
    • one year ago
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    Correct. Between 3/2, 1/2 and 1, 3/2 is largest.

  18. mathstudent55
    • one year ago
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    You're welcome.

  19. anonymous
    • one year ago
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    you were alot of help thanks so much

  20. mathstudent55
    • one year ago
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    You're welcome,

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