Algebra Problems, HELP?

1) Write an equation of the line containing the given point and parallel to the given line. Express your answer in the form y = mx + b

(4,5); x + 7y = 4

The equation of the line is y = ?

2) Find an equation of the line having the given slope and containing the given point.

m = 5/6, (3, -5)

3) find an equation of the line containing the given pair of points.

(-1,-6) and (-4, -7)

The equation of the line is y = ?

4) Find an equation of the line containing the given pair of points.

[ 1/4, - 1/2] and [ 3/4, 4]

What is the equation of the line?

y=

(simplify all answers)

Please explain how you got the answer in each question (step by step). I really appreciate any help you give.

Comments

  • all these can be done with the following formulas:

    y - y1 = m(x - x1) and m = (y2 - y1) / (x2 - x1)

    y - 5 = (-1 / 7)(x - 4)

    y - 5 = ( - 1 / 7)x + 4 / 7

    y = ( -1 / 7)x + (39 / 7)

  • 1) (4,5); x + 7y = 4

    Put the equation in point-slope form (solve for y)

    x + 7y = 4

    7y = -x + 4

    y = -1/7 * x + 4/7

    The slope of the line is -1/7, so the slope of the parallel line is -1/7. Plug in -1/7 for m and (4,5) for x and y to find b.

    y = mx + b

    5 = -1/7 * 4 + b

    5 = -4/7 + b

    b = 5 + 4/7

    b = 39/7

    The equation of the line is y = -1/7 * x - 39/7

    2) Same as the second part of #1. Plug the numbers into y = mx + b.

    6 = 5/6 * 3 + b

    6 = 15/6 + b

    b = 6 - 15/6

    b = 21/6

    b = 7/2

    y = 5/6 * x + 7/2

    3) (-1,-6) and (-4, -7). First find the slope.

    m = (y2 - y1) / (x2 - x1)

    m = (-7 - (-6)) / (-4 - (-1))

    m = -1 / -3

    m = 1/3

    Plug in m and one of the points to find b.

    y = mx + b

    -6 = 1/3 * (-1) + b

    b = -6 + 1/3

    b = -17/3

    The equation of the line is y = 1/3 * x - 17/3

    4) (1/4, -1/2) and (3/4, 4). Same thing. Find the slope first.

    m = (4 - (-1/2)) / (3/4 - 1/4)

    m = 7/2 / 1/2

    m = 7

    Find b

    -1/2 = 7 * 1/4 + b

    b = -1/2 - 7/4

    b = -9/4

    What is the equation of the line? y = 7x - 9/4

    I hope I explained it clearly enough.

Sign In or Register to comment.