Equation in Slope-Intercept form?

I need help understanding how to work these types of problems out:

Write an equation in slope-intercept form of the line that passes through the given point and is parallel to the graph of each equation.

2x + y = 5; (3, 1)

Write an equation in slope-intercept form of the line that passes through the given point and is perpendicular to the graph of each equation.

x - 6y = 2; (2, 4)

Thank you!

3 Answers

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  • 1 decade ago
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    slope-intercept form -> y=mx+b

    2x+y = 5

    y = -2x + 5

    So, the slope of our line is -2x; therefore, a line parallel to this one MUST have the same slope (check on paper!). We know it passes through the point (3,1) where x = 3, and y =1

    using point-slope formula:

    y-1 = -2(x-3)

    y=-2x+7

    next problem:

    x-6y=2

    -6y=-x+2

    y=(x/6)-(1/3)

    slope = 1/6

    We know that the slope of the line we have times the slope of a perpendicular line we are trying to find will be = -1. You can verify this from your textbook or an online source. Let M be the slope of the perpendicular line we are trying to find:

    1/6(m) = -1 from our identity above

    m = -6 which is the slope of our perpendicular line

    We know it passes through the point (2,4) so we use point-slope formula again:

    y-4=-6(x-2)

    y=-6x+12+4

    y=-6x+16

  • 1 decade ago

    Find the slope of the given equation, then plug that into a new equation that should look like (in the case of your first problem)

    y= -2x + b <y-intercept

    ^

    slope

    Then find b, by graphing, mental work, or just plug in the coordinates into the new equation.

    (3,1) 1 = -2(3) + b Solve for b (it should be 7)

    x y

    For the second one you need to use the opposite reciprocal of the slope and do the same thing.

    Opposite= negative of whatever it is referring to

    Reciprocal= The number one divided by whatever it is referring to

    The opposite reciprocal of that slope would be -6.

    Math dominates, JONNy-G

  • 1 decade ago

    Do your own homework man!!

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