math (algebra)

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write an equation of the line containing the given point and parallel to the given line.

(7,8); x+5y=2

(-2,4); 9x=5y+3

(3,5); 8x+y=2

(5,-3) 9x+4y=3

I am not sure how to do them

  • math (algebra) -

    The key point to know is that:

    if the new line is parallel, then the coefficients of x and y will be the same

    (The coefficients are the numbers that x and y are multiplied by).

    So, taking the first one, any line parallel to x+5y=2 will be of the form

    x + 5y = some_number

    x + 5y = -20

    x + 5y = 3.14159

    x + 5y = 0

    are all parallel.

    So to find the parallel line that goes through (7,8) we just have to find the specific number that makes such a line go through that point.

    That point has x=7, y=8, so we need to plug those into the equation form that we know:

    x + 5y = something

    7 + 5 * 8 = something

    7 + 47 = something = 47

    So a line parallel to x+5y=2, containing (7,8) is x+5y=47.

    Now try the others yourself.

  • math (algebra) -oops -

    I typoed, and it might confuse you. Sorry. 5*8 is 40, or course, not 47.

    x + 5y = something

    7 + 5 * 8 = something

    7 + 40 = something = 47

    So a line parallel to x+5y=2, containing (7,8) is x+5y=47.

  • math (algebra) -

    I am so lost. i have to type my answers in point slope form (y=mx+b)

  • math (algebra) -

    That's OK. First you solve it. Then you put it into the form you need.

    Point slope form just means moving y to the left hand side, and everything else to the right.

    Consider:

    x + 5y = 47

    Subtract x from both sides:

    5y = 47 -x

    Divide by 5

    y = 47/5 - x/5

  • math (algebra) -

    I am still lost sorry.

  • math (algebra) -

    Take the next one then. Step by step.

    9x = 5y + 3

    Parallel, but going through (-2, 4).

    x is -2. y is 4.

    It must be

    9x = 5y + something

    9*-2 = 5*4 + something.

    What is the something?

  • math (algebra) -

    no idea

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