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# What is the equation of the line that passes through (-8,9) and (10,-3)?

I am confused how to find "b". The answer is in point-slope form but i don't know how to get there. HELP!!! thx
Member since:
February 27, 2006
Total points:
3,333 (Level 4)

## Best Answer - Chosen by Voters

m = (-3-9)/(10-(-8)) = -12/18 = -2/3

equation :

y - 9 = (-2/3) [x-(-8)]
y-9=(-2/3)(x+8)

solve it and get the equation-
3y-27=-2x-16
2x+3y=11

or

y = -(2/3)x + 11/3
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### Other Answers (6)

• Member since:
October 05, 2007
Total points:
5,963 (Level 5)
By letting p1=( -8, 9 ) and p2 = ( 10, -3 ), we have the slope of

m = change y / change x = -2/3

Using p1 ( -8, 9 ) in the point-slope formula, we have:

( y - 9 ) = -2/3 ( x - 8 )

solving for y = -2/3 x + 11/3 ( y - intercept is b = 11/3 when x =0 )

Using p2 ( 10, -3 ) in the point-slope formula yields us once again....

( y + 3 ) = -2/3 ( x - 10 ) expanding and collecting the like terms we obtain

y = -2/3 x + 11/3 ( y-intercept b = 11/3 when x =0 )

multiplying both sides of the equation by 3, we have:

3y = -2x + 11

therefore, the equation of the line that passes through the
points ( -8, 9 ) and ( 10, -3 ) is:

2x +3y - 11 = 0

### Source(s):

0% 0 Votes
• by DrGerard
Member since:
May 07, 2006
Total points:
6,389 (Level 5)
Let me give you TWO methods, in detail:

FIRST METHOD:
The equation is y = m x + b
The line passes through (-8,9) and (10,-3) when both of the following equations hold:
9 = -8 m + b
-3 = 10 m + b

Substract those two equations from each other to eliminate b. You obtain: 12 = -18 m, or m = -2/3.

Plug that value of m into either equation to obtain the value of b, namely (using the first equation): 9 = -8 (-2/3) + b, so:
b = 9-16/3 = 11/3

If you prefer, you can also obtain the value of b directly by eliminating m between the two equations (multiply the first by 5 and the second by 4 and add them up). You obtain: 45-12 = 9 b, so b = 11/3, indeed.

SECOND METHOD (more efficient):
At a slightly more advanced level, we may obtain the equation of the line directly by stating that (x+8, y-9) is proportional to (10+8,-3-9). If you know what a determinant is, you may just write that the relevant 2 by 2 determinant is zero. Otherwise, just write that the proportionality means:
(x+8)(-3-9) = (y-9)(10+8)
Just simplify that:
-12 (x+8) = 18 (y-9) or 2(x+8)+3(y-9) = 0
This boils down to 2x+3y=11

You may keep this equation as is or divide by 3 to put it in the form
y = (-2/3)x+(11/3) or y = (11-2x) / 3

RECOMMENDATIONS:
I advise you to get familiar with the second method ASAP and, also, to acquire a taste for the nicer form of the equation of a line where the coefficient of y need not be 1. Here: 2x+3y=11.

Last step: Check that the equation obtained holds for both points:
2(-8) + 3(9) = 11
2(10) + 3(-3) = 11

Trimming all the fat, the entire computation merely consists in simplifying a single line, as shown in the link below:

### Source(s):

20% 1 Vote
• by Bonnie K
Member since:
June 27, 2008
Total points:
632 (Level 2)
First, you have to figure out what the slope is. The formula for doing that is this: y2-y1/x2-x1 = the slope of the line. OK?

So, lets use the first point as (x1, y1) and the second point as (x2, y2).

Considering that, we'd have -3-9/10-(-8) = -12/18 = -2/3 = slope

Now, use the point/slope forumula to get the equation you need.

Here it is: y-y1 = m(x-x1)

The first y and x stay just that way, as y and x. The y1 and x1 are the coordinates of whichever point given you choose to work with. I'll choose point #2.

y - 9 = m(x - (-8))
y - 9 = -2/3(x + 8)

now multiply the right side out:

y - 9 = -2/3 x - 16/3

The form you want to put this in is y = mx + b, I know this because you mentioned b in your question. b indicates the y intercept of the line between these 2 points.

So, now you have to add 9 to both sides of the equation above to get it in the form of y = mx + b:

y -9 +9 = -2/3 x - 16/3 + 9

y = -2/3 x - 16/3 + 27/3

y = -2/3 x + 27/3 - 16/3

y = -2/3 x + 11/3 Done!

### Source(s):

BS math, teacher
0% 0 Votes
• by jaya
Member since:
February 17, 2007
Total points:
4,206 (Level 4)
First find the slope 'm'

m =( y" -y') /( x"-x') = -3-9 / 10-(-8) = -12 / 18 = -2/3

so the equation in slope-intercept form will be

y = -2x/3 + b

now substitute x=-8 and y=9

9 = -2x-8 /3 +b

9 = 16/3 +b

b = 9-16/3

b = (27-16)/3

b = 11/3

so the equation of the line is y = -2x/3 +11/3

or , 3y +2x = 11
20% 1 Vote
• Member since:
October 29, 2006
Total points:
2,736 (Level 4)
First find m, or the slope.

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

m = (-3 - 9) / (10 - (-8) )

m = -12 / 18

m = -2/3

Point slope form:

(y - y1) = m (x - x1)

Pick an ordered pair. I'll pick (-8, 9)

(y - 9) = (-2/3) (x - -8)

(y - 9) = (-2/3) (x + 8)

y - 9 = (-2/3)x - 16/3

y = (-2/3)x - 16/3 + 9

y = (-2/3)x + 11/3
0% 0 Votes
• Member since:
July 29, 2008
Total points:
3,239 (Level 4)
first find the slope: rise over run y2-y1/ x2-x1
y-9= -2/3 ( x- (-8) )

y-9= -2/3x -16/3
add 9 to get y by itself

y= -2/3x + 11/3
0% 0 Votes

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