Algebra

I have an assignment that asks me to write an equation in slope-intercept, point-slope, or standard form for the information given and to explain why the chosen form would be best. Below is the information given.

1. passing through (-1,4) and (-5,2)
2. that has slope 2 and y intercept 4
3. that has an x-intercept of 6 and a y-intercept of 3
4. that passes through (1,2) and has a slope of -5/3

I chose point-slope for the first one, slope-intercept for the second, slope-intercept for the third, and point-slope for the fourth. Do you think my answers are good, or would you choose different forms for some of them?

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  1. actually, any method should work for any of those conditions,
    in #3, I would use the intercept-intercept form
    if the x-intecept is 'a' and the y-intercept is 'b', then the equation can be written simply as
    x/a + y/b = 1
    so x/6 + y/3 = 1
    times 6
    x + 2y = 6 , all done!

    If I know the slope and a point, I use a method that given me the equation in about 3 lines
    - based on the fact that for
    Ax + By = C, the slope is -A/B
    if you give me the slope I can reverse that and start with the completed left side of the equation,

    e.g.
    given slope as -5/3 and the point (1,2) , your #4
    the equation has to be
    5x + 3y = C , but (1,2) lies on it, so
    5(1) + 3(2) = C
    C = 11
    equation: 5x + 3y = 11

    advantage, no fractions!

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  2. Thanks again!

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