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A line is parallel to 5x+2y-8=0 and has the same y-intercept as x+4y-12=0
Find an equation for the line.

  • Math -

    first make each into y=mx+b by rearranging

    5x+2y-8=0
    2y=-5x+8
    y=-5/2x +4

    and

    x+4y-12=0
    4y=-x+12
    y=-1/4x+3

    because the line is parallel to the first equation it will have the same value for the slope (m)

    y=-5/2x+b

    now use the second equation to solve for the value of y at the y intercept (i.e. we know x is zero, solve y)

    y=-1/4x+3
    y=-1/4(0)+3
    y=3

    so the y intercept of our new equation is (x,y)=(0,3)

    put this into our new equation to solve for b

    y=-5/2x+b
    3=-5/2(0)+b
    3=b

    so our new equation is

    y=-5/2x+3

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