Mathematics

Question

What is an equation of the line that passes through the point (-2, 1) and is parallel to the line whose equation is 4x-2y=8?

2 Answer

  • Answer:

    y-1=2(x+2)

    Step-by-step explanation:

    4x-2y=8

    2y=4x-8

    y=4/2x-8/2

    y=2x-4

    ---------------

    Parallel means same slope.

    m=2

    y-y1=m(x-x1)

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

    y-1=2(x+2)

  • Parallel lines have the same slope

    The equation of the line is: [tex]y = 2x+5[/tex]

    The equation is given as:

    [tex]4x - 2y =8[/tex]

    Divide through by 2

    [tex]2x - y =4[/tex]

    Make y the subject

    [tex]y = 2x - 4[/tex]

    Because the required equation and [tex]y = 2x - 4[/tex] are parallel, then they must have the same slope

    A linear equation is represented as:

    [tex]y = mx + c[/tex]

    Where:

    [tex]m = slope[/tex]

    So, by comparison

    [tex]m = 2[/tex]

    This means that the slope of the required line is 2

    The equation is then calculated as:

    [tex]y = m(x - x_1) + y_1[/tex]

    So, we have:

    [tex]y = 2(x--2) + 1[/tex]

    [tex]y = 2(x+2) + 1[/tex]

    Open brackets

    [tex]y = 2x+4 + 1[/tex]

    [tex]y = 2x+5[/tex]

    Hence, the equation of the line is: [tex]y = 2x+5[/tex]

    Read more about equations of parallel lines at:

    https://brainly.com/question/402319

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