Question

A line contains the points (3,9) and (-1,1) what is the equation of the line?

Answer 1

(3,9)(-1,1)
slope = (1 - 9) / (-1 - 3) = -8/-4 = 2

y = mx + b
slope(m) = 2
(3,9)...x = 3 and y = 9
now we sub and find b, the y int
9 = 2(3) + b
9 = 6 + b
9 - 6 = b
3 = b

so ur equation is : y = 2x + 3

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3x - y = 6
3x + 6 = y...rearrange to : y = 3x + 6 <== slope intercept form

Answer 2

To find the equation of a line using two given set of points, you must first find slope. To do so, we must use the slope formula:
y2 - y1 / x2 - x1 

In this case:
1 - 9 / -1 - 3 = -8 / -4 
- 8 / -4 = 2 (simplified) 

Now we can use the point-slope formula:
y - y1 = m(x - x1) 

y - 1 = 2(x + 1 )
y - 1 = 2x + 2
y = 2x + 3

In order to make 3x - y = 6 in slope intercept form, we must isolate y.

- y = -3x + 6
Note: y cannot be negative, so we'll multiply both sides by -1 
( -1 ) - y = - 3x + 6 ( -1 ) = y = 3x -6