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Math Help - Equation Of The Line?

  1. #1
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    Equation Of The Line?

    hi im new on here,

    i have two questions i am stuck on and would like your help :

    here are the qestions:

    1.the line y=1/4 x +2 meets the y axis at the point B. the point C has co ordinates (-5,3). find the gradient of the line joining points B and C .

    2.the lines y= x and y=2x-5 intersect at the point A . find the equation of the line with gradient 2/5 that passes through the point A . ( Hint : solve y=x and y= 2x-5 simultaneously.)

    please help me by showing me how you worked it out

    thank you
    Last edited by mr fantastic; September 12th 2011 at 12:17 AM. Reason: Title.
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  2. #2
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    Re: Equation Of The Line?? Help Please!

    Quote Originally Posted by MathsFreakLove View Post
    hi im new on here,

    i have two questions i am stuck on and would like your help :

    here are the qestions:

    1.the line y=1/4 x +2 meets the y axis at the point B. the point C has co ordinates (-5,3). find the gradient of the line joining points B and C .

    2.the lines y= x and y=2x-5 intersect at the point A . find the equation of the line with gradient 2/5 that passes through the point A . ( Hint : solve y=x and y= 2x-5 simultaneously.)

    please help me by showing me how you worked it out

    thank you
    1. What is the y intercept of \displaystyle y = \frac{1}{4}x + 2? How do you find the gradient of a line that passes through two points?
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  3. #3
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    Re: Equation Of The Line?? Help Please!

    Quote Originally Posted by MathsFreakLove View Post
    i have two questions i am stuck on and would like your help :

    here are the qestions:

    1.the line y=1/4 x +2 meets the y axis at the point B. the point C has co ordinates (-5,3). find the gradient of the line joining points B and C .

    point B is the y-intercept of the line ... you should be able to recognize that value since the line's equation was given in slope-intercept form.

    once you determine the coordinates of the y-intercept, use the equation to determine the slope between two points in the x-y plane.


    m = \frac{y_2-y_1}{x_2-x_1}

    2.the lines y= x and y=2x-5 intersect at the point A . find the equation of the line with gradient 2/5 that passes through the point A . ( Hint : solve y=x and y= 2x-5 simultaneously.)

    set x = 2x-5 to determine the x-value of intersection, then use either line to determine the y-value of intersection. once you get those coordinates, use the point-slope form of a linear equation to find the desired equation ...

    y - y_1 = m(x - x_1) , where (x_1,y_1) is the point of intersection and m is the given slope.
    let's see what you can do
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