I need math help. with the given information I need to make a general form Ax+By=C?

Ax+By=C form

4. (7,-2) m=8/7

8. (1,-1) (4,5)

10.(9,0) (-3,4)

Now I need these in this form y=Mx+B

7. (-7, 7) (9, -3)

9.(-6, -4) (-2, -2)

I would love it if you would explain how you got your answer thanks

2 Answers

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  • 1 decade ago
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    Ax + By = C

    Let's convert the equation above to slope-intercept form. Then we can see what's going on:

    By = -Ax + C

    y = -A/B x + C/B

    y = mx + b

    4.

    We can see from above that m actually is equal to -A/B, and b = C/B. We are given m = 8/7, and since m is a positive number, then m = -(-A/B) = 8/7 = -(-8/7). Hence A = -8 and B = 7. Using that information, and the given (x, y) values, we can determine C:

    A = -8; B = 7; x = 7; y = -2

    y = -A/B x + C/B

    -2 = [-(-8)/7] (7) + C/B

    -2 = 8 + C/B

    -2 - 8 = C/B

    -10 = C/B

    -10 B = C

    -10 (7) = C

    -70 = C

    Now we have everything we need to write the equation:

    Ax + By = C

    -8x + 7y = -70.

    Now we can check the equation to see if it is correct. If we plug x = 7 into the equation, then y = -2 should be returned.

    -8 (7) + 7y = -70

    -56 + 7y = -70

    7y = -70 + 56

    7y = - 14

    y = -14/7

    y = -2

    The correct value for y was returned, so the equation is -8x + 7y = -70.

    8.

    First find m. m = [5 - (-1)]/(4 - 1) = (5 + 1)/(4 - 1) = 6/3 = 2. Now using the slope-intercept form for the equation of a line, and either of the two (x, y) point coordinates, we get this:

    Ax + By = C

    y = -A/B x + C/B

    Since -A/B = m = 2, then A = -2, and B = 1.

    y = -(-2/1) x + C/1

    y = 2x + C.

    Using (1, -1) for x and y, we get this:

    -1 = 2 (1) + C

    -1 = 2 + C

    -1 - 2 = C

    -3 = C.

    Now we have all the parts for this equation we need:

    -2x + y = -3.

    To verify, use the other point, and let x = 4. Then y = 5 should be returned:

    -2 (4) + y = -3

    -8 + y = -3

    y = -3 + 8

    y = 5.

    The correct y value is returned, so the correct equation is -2x + y = -3.

    10.

    Work this problem the same way we did #8.

    7.

    First find M:

    M = (-3 - 7)/(9 + 7) = -10/16 = -5/8.

    The following equation results:

    y = Mx + B

    y = -5/8 x + B.

    Let x = -7 and y = 7 from the first point, and solve for B:

    y = -5/8 x + B

    7 = -5/8 (-7) + B

    7 = 35/8 + B

    (56 - 35)/8 = B

    21/8 = B.

    y = -5/8 x + 21/8

    Now use the x and y coordinates of the second point to verify the equation. If it is correct, then y = -3 should be returned:

    y = -5/8 (9) + 21/8

    y = -45/8 + 21/8

    y = (-45 + 21)/8

    y = -24/8

    y = -3

    9.

    This problem is worked the same way as #7.

    Good luck with the rest of your homework. If you have any other questions concerning these problems, e-mail me via my profile.

  • 4 years ago

    I continually problem of a line as y = m * x + b, the position m is the slope and b is the y-intercept. So right here we may have y = 3x + 2. Rearrange so that you've 0 on the right hand side: -3x + y - 2 = 0. it truly is an similar as d).

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