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bealiberty47

  • one year ago

Math function rule question

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  1. bealiberty47
    • one year ago
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  2. mathstudent55
    • one year ago
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    First, look at the points you are given. Do they seem to be linear or not? To see if they are linear, see if the same change in x has the same change in y.

  3. mathstudent55
    • one year ago
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    If they are linear, then choose two points and find the equation of the line through them.

  4. bealiberty47
    • one year ago
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    There isn't a same change because while Y goes up x2, X goes down randomly

  5. bealiberty47
    • one year ago
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    So it's not linear?

  6. bealiberty47
    • one year ago
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    can you help me @geerky42

  7. bealiberty47
    • one year ago
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    @mathstudent55

  8. mathstudent55
    • one year ago
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    No. Don't compare with multiplication. Compare with subtraction.

  9. Pawanyadav
    • one year ago
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    Try to plot its graph it clarify everything to you

  10. mathstudent55
    • one year ago
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    Here are the points: x 2 4 6 y 1 0 -1

  11. mathstudent55
    • one year ago
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    I will write the differences between each x-coordinate and the previous one on the line above the x-coordinates. I will do the same for the y-coordinates below the y-coordinates 2 2 x 2 4 6 y 1 0 -1 -1 -1

  12. mathstudent55
    • one year ago
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    Notice that as x goes from 2 to 4, the difference is 2. As x goes from 4 to 6, the difference is again 2. Now look at y. As x goes from 2 to 4, y goes down by 1. As x goes from 4 to 6, y again goes down by 1. Every time x increases 2, y decreases 1. That is a linear relation.

  13. bealiberty47
    • one year ago
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    x + 2 = y - 1

  14. mathstudent55
    • one year ago
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    Now that you see it's a linear relation, pick any two points. Then find the slope of the line between the two points. Do you know how to find the slope of a line given two points on the line?

  15. bealiberty47
    • one year ago
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    no please explain

  16. mathstudent55
    • one year ago
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    For points \((x_1, y_1)\) and \((x_2, y_2) \), the slope opf the line through those points is: \(slope = m = \dfrac{y_2 - y_1}{x_2 - x_1} \) In other words, subtract the y-coordinates. Subtract the x-coordinates.. Divide the first difference by the second difference.

  17. mathstudent55
    • one year ago
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    That gives you slope. Then we have a little more work to find the equation.

  18. bealiberty47
    • one year ago
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    just give me a minute

  19. bealiberty47
    • one year ago
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    4,0 - 2,1 = -1/2?

  20. bealiberty47
    • one year ago
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    or is it 2,1 - 4,0 = 1/2

  21. bealiberty47
    • one year ago
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    @mathstudent55

  22. mathstudent55
    • one year ago
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    If you use the points (4, 0) and (2, 1), you get: \(m = \dfrac{0 - 1}{4 - 2} = \dfrac{-1}{2} = -\dfrac{1}{2} \)

  23. mathstudent55
    • one year ago
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    The slope is -1/2 Now we need to get the equation of the line. The slope-intercept form of the equation of t a line is \(y = mx + b\), where m = slope and b = y-intercept. We know the slope is -1/2. We need to find b. We use one of our 3 points in the equation and solve for b. \(\color{red}{y} = \color{green}{m}\color{blue}{x} + \color{brown}{b}\) Let's use point \((\color{blue}{4}, \color{red}{0})\). We replace \(\color{blue}{x}\) with \(\color{blue}{4} \) and \(\color{red}{y} \) with \(\color{red}{0}\). We replace \(\color{green}{m}\) with \(\color{green}{-\dfrac{1}{2}}\), since \(\color{green}{m}\) is the \(\color{green}{slope}\) and the \(\color{green}{slope}\) is \(\color{green}{- \dfrac{1}{2}} \). \(\color{red}{0} = \color{green}{-\dfrac{1}{2}} (\color{blue}{4}) + \color{brown}{b}\) \(0 = -2 + b\) \(b = 2\) Now that we know b = 2, we can write the equation of the line: \(y = -\dfrac{1}{2}x + 2\)

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