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Math Help - Linear equations in two variables

  1. #1
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    Linear equations in two variables

    Find the x and y intercepts and slope (if they exist) for the line given.
    -2x + y = 14
    x intercept Would it be (-2,0)
    y intercept Would it be ( 0,4)
    Slope Would it be 2

    The slope of a line is 1/3
    What is the slope of a line parallel to the given line? Would it be 1/3
    What is the slope of a line perpendicular to the given line? Would it be -1/3

    What if the slope (if it exists) of a line given by the equation x = -5? Would it be undefined?
    Thanks
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  2. #2
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    Quote Originally Posted by rowdy3 View Post
    Find the x and y intercepts and slope (if they exist) for the line given.
    -2x + y = 14
    x intercept Would it be (-2,0)
    y intercept Would it be ( 0,4)
    Slope Would it be 2
    These points aren't even on the line! How can they be intercepts??

    You got the slope right, though.
    y = 2x + 14
    The x-intercept is where y = 0. Solve this for x.
    The y-intercept is where x = 0. Solve this for y.

    Quote Originally Posted by rowdy3 View Post
    The slope of a line is 1/3
    What is the slope of a line parallel to the given line? Would it be 1/3
    What is the slope of a line perpendicular to the given line? Would it be -1/3
    Yes to the first, no to the second. Two perpendicular lines have slopes that have the following property:
    m_1m_2 = -1

    So you know that m_1 = 1/3.
    \frac{1}{3} \cdot m_2 = -1
    Solve for m_2.

    Quote Originally Posted by rowdy3 View Post
    What if the slope (if it exists) of a line given by the equation x = -5? Would it be undefined?
    Thanks
    Yes. The slope of a line is rise/run. Consider two points on this line, say (-5, 1) and (-5, 6).
    \text{slope} = \frac{1 - 6}{-5 - (-5)} \to \frac{-5}{0}
    which is undefined.

    -Dan
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  3. #3
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    This is what I did.
    y= 2x + 14
    x- intercept 0= 2x + 14 14/2
    x- intercept (7,0)
    y- intercept y= 2(0) + 14
    y- intercept (0,14)

    The slope of a line is 1/3
    1/3 * - 3/1 =-1
    What is the slope of a line perpendicular to the given line? Is it -3/1
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    Quote Originally Posted by rowdy3 View Post
    This is what I did.
    y= 2x + 14
    x- intercept 0= 2x + 14 14/2
    x- intercept (7,0)
    y- intercept y= 2(0) + 14
    y- intercept (0,14)

    The slope of a line is 1/3
    1/3 * - 3/1 =-1
    What is the slope of a line perpendicular to the given line? Is it -3/1
    This is correct except for your x-intercept. Again, \left(7,\;0\right) isn't even on the line (since 0\neq2\cdot7 + 14). Your method is fine, but you made a slight mistake when solving for x.
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  5. #5
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    Write an equation of the line passing through the point (12, -10) having slope 4/3. Write your final answer in slope-intercept form.

    Write an equation of the line passing through the point (0, 2) and parallel to the line x-y = 7. Write your final answer in slope-intercept form.

    1. y+10= 4/3 ·(x- 12) My answer is y= 4/3·x -26

    2. P(0,2) slope= 1--> y-2= 1(x-0) My answer is y= x + 2
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  6. #6
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    Quote Originally Posted by rowdy3 View Post
    Write an equation of the line passing through the point (12, -10) having slope 4/3. Write your final answer in slope-intercept form.

    Write an equation of the line passing through the point (0, 2) and parallel to the line x-y = 7. Write your final answer in slope-intercept form.

    1. y+10= 4/3 ·(x- 12) My answer is y= 4/3·x -26

    2. P(0,2) slope= 1--> y-2= 1(x-0) My answer is y= x + 2
    Everything is OK

    By the way: If you have a new question start a new thread. Otherwise you risk that no member of the forum will see that you need some additional help.
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