geometry

Use the equation and given point to answer the questions below.

The equation of line a is y=12x−1, and it passes through point (6,2).
Line b is perpendicular to line a, and it passes through point (−6,2).
A: What is the slope of line b?
B: What is the y-intercept of line b?
Select two answers: one for A and one for B.

B: 14
B: 1
A: 1/2
A: −2
A: −1/2
B: 5
A: 2
B: -1

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  1. Sorry line A is Y=1/2x-1

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  2. Recall that lines with slopes m1 and m2
    are parallel if m1 = m2
    are perpendicular if m1 * m2 = -1

    so, since line A has slope 1/2, B has slope -2
    Now for line B, you have a point (-6,2) and a slope (-2). Using the point-slope form, that makes B's equation
    y-2 = -2(x+6)
    Rearrange that into the slope-intercept form, and you have
    y = -2x - 10
    the y-intercept is seen to be -10

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  3. A straight line in the form y = mx + b, has a slope of m and a y-intercept of b
    so y = (1/2)x - 1 has a slope of 1/2 and a y-intercept of -1

    Parallel lines have the same slope, so the slope of your new line is also 1/2
    and it must be y = (1/2)x + b, but it passes through the new point (-6,2)
    then 2 = (1/2)(-6) + b
    2 = -3 + b
    b = 5
    so your 2nd line equation is y (1/2)x + 5

    fit it all together to answer your question

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    Reiny
  4. argghhh, I read it as parallel
    so go with oobleck's way

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    Reiny
  5. perpendicular lines have negative reciprocal slope. for line b slope then is -2. What is the y-intercept of line b? y=-2x+b and the point (−6,2) is one it, then
    2=-2(-6)+b or b= 12+2 = 14

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    bobpursley

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