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# 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

- MathBioMajorLv 71 decade agoFavorite Answer
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.

- nichollsLv 44 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).