Anonymous
Anonymous asked in Science & MathematicsMathematics · 6 years ago

Help i dont get these math questions.?

Write the equation of the line described in slope-intercept form.

A) The line with zero slope and y intercept 5.

B) The perpendicular bisector pf the segment joining (0,8) and (2,-4).

C) The line with y intercept 2 and parallel to 6x-2y=6

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  • 6 years ago
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    slope-intercept form of a line is y=mx + b

    where m is the slope and b is the y value at which the line crosses the y axis, which is also x = 0.

    Recall that slope is the change of the y value divided by the change of the x value between two points.

    A zero slope means y does not change between 2 given points on a line. A zero slope line is level.

    That means the line is flat all across the graph and is equal to a single y value.

    If a line of zero slope and a y intercept of 5, that means the line has the y value of 5 everywhere for all x values.

    So m = 0 and b = 5 y = 0x + 5 or y = 5.

    B) Perpendicular lines have slopes that are negative reciprocals of each other. That means that if the slope of one line is 3, the slope of a line perpendicular to it will be -1/3 . Recall that perpendicular lines cross at right angles (90 degrees) to each other.

    First determine the slope and bisector (mid-point) of the line segment joining (0,8) and (2, -4).

    Again, the slope is the change in y over the change in x.

    (-4 - 8) / (2 - 0) = -12 / 2 = -6

    The mid-point is just half of the distance between the x and y values.

    The distance between 2 and 0 is 2, so the mid-point at x is 1.

    The distance between 8 and -4 is 12, so the mid-point at y is 8 - 6 = 2.

    So the perpendicular bisector will have a slope of 1/6 and intersect at the mid-point (1,2)

    The y intercept of the perpendicular line will have an x value of 0.

    So using the slope formula (2 - y) / (1 - 0) = 1/6 , we can find the y intercept.

    (2 - y) / 1 = 1/6 -> 2 - y = 1/6

    -y = 1/6 - 2 or y = 2 - 1/6 = 11/6

    So y = 1/6 x + 11/6

    c) Parallel lines have the same slope.

    6x - 2y = 6 in slope intercept form is

    -2y = 6 - 6x -> y = -3 + 3x -> y = 3x -3

    So the y intercept is -3 and the slope is 3 .

    The line we are trying to express has a y intercept of 2 so plug that into the formula

    y = 3x + 2

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  • iceman
    Lv 7
    6 years ago

    A) y = 5

    B) m = (-4 - 8)/(2 - 0) = -5

    m of perpendicular = 1/5

    mid point: [(0 + 2)/2 , (8 - 4)/2] = (1 , 2)

    y - 2 = 1/5(x - 1)

    y = (1/5)x + 9/5

    C) 2y = 6x - 6

    y = 3x - 3

    m = 3 , b = 2

    y = mx + b

    y = 3x + 2

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