# Find an equation for the line that passes through the points , (1, -2 ) and , (−5, 6)?

### 5 Answers

- billrussell42Lv 71 month agoFavorite Answer
Two points form of line

y – y₁ = (x – x₁)(y₂ – y₁) / (x₂ – x₁)

y + 2 = (x – 1)(6 + 2) / (–5 – 1)

y + 2 = (x – 1)(8) / (–6)

y + 2 = (–4/3)(x – 1)

3y + 6 = –4x + 4

3y + 4x + 2 = 0

or

3y = – 4x – 2

y = –(4/3)x – (2/3)

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- PopeLv 71 month ago
(6 + 2)(x - 1) - (-5 - 1)(y + 2) = 0

8x - 8 + 6y + 12 = 0

8x + 6y + 4 = 0

4x + 3y + 2 = 0

Suit yourself, but I prefer general form. Notice that it involves no division, so there is no risk of division by zero. Also, given integer coordinates, there are no fractional coefficients involved.

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- KrishnamurthyLv 71 month ago
The equation of the line that passes through the points, (1, -2) and , (−5, 6):

The Points are (1 , 4) and (7, 5)

Slope of the line is (6 − -2)/(-5 − 1) = 8/-6 = -4/3

Equation of line is ( y − 4 ) = 1 6 ( x − 1 ) 6 y −24 =

x

−

1

x

−

6

y

+

23

=

0

We can use the point-slope formula to write an equation for this line.

The point-slope formula states:

(y − y1) = m(x − x1)

Where

m is the slope and (x1 , y1) is a point the line passes through.

Substituting the slope and values from the point in the problem gives:

( y − −2) = 3(x − 1)

( y + 2) = 3(x + 5 )

We can solve for y if we need to show the equation in slope-intercept form.

The slope-intercept form of a linear equation is:

y = m x + b

Where m is the slope and b is the y-intercept value.

y + 9 = ( 3 × x ) + ( 3 × 5 )

y + 9 = 3 x + 15

y + 9 − 9 = 3 x + 15 − 9

y + 0 = 3 x + 6

y = 3 x + 6

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- 1 month ago
m = (6 - (-2)) / (-5 - 1)

m = (6 + 2) / (-6)

m = 8/(-6)

m = -4/3

y - k = m * (x - h)

(h , k) is a point on the line

y - (-2) = (-4/3) * (x - 1)

y + 2 = (-4/3) * x + (4/3)

y = (-4/3) * x + (4/3) - 2

y = (-4/3) * x - (2/3)

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