find the equation of the line

1.(-2,-8) and (-5,-6)

2.(-1,-1) and (2,2)

3. 6/7, (1,-8)

4.9, (9,1)

you don't specify what form you want it, so I will do it the general way, which will leave you without fractions.

I will do the first one, do the others the same way

slope = (-6+8)/(-5+2) = -2/3

y+8 = (-2/3(x+2)
3y + 24 = -2x - 4
2x + 3y + 28 = 0
or
y = (-2/3)x - 28/3 after re-arranging the equation

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To find the equation of a line, we can use the slope-intercept form, y = mx + b, where m represents the slope of the line and b represents the y-intercept.

To find the slope (m), we can use the formula: m = (y2 - y1)/(x2 - x1), where (x1,y1) and (x2,y2) are two points on the line.

1. For the points (-2, -8) and (-5, -6):
m = (-6 - (-8))/(-5 - (-2))
= (-6 + 8)/(-5 + 2)
= 2/-3
= -2/3

Now that we have the slope, we can substitute it and one of the given points into the slope-intercept form to find the y-intercept (b). Let's use (-2, -8):
-8 = (-2/3)(-2) + b
-8 = 4/3 + b
b = -8 - 4/3
b = -32/3 - 4/3
b = -36/3
b = -12

The equation of the line is y = (-2/3)x - 12.

2. For the points (-1, -1) and (2, 2):
m = (2 - (-1))/(2 - (-1))
= (2 + 1)/(2 + 1)
= 3/3
= 1

Using (-1, -1) to find b:
-1 = 1(-1) + b
-1 = -1 + b
b = -1 + 1
b = 0

The equation of the line is y = x + 0, which simplifies to y = x.

3. For the point (6/7, 1) and (-8):
m = (1 - (-8))/(6/7 - (-8))
= (1 + 8)/(6/7 + 56/7)
= 9/(6/7 + 56/7)
= 9/(62/7)
= 9 * 7/62
= 63/62

Using (6/7, 1) to find b:
1 = (63/62)(6/7) + b
1 = 378/434 + b
b = 1 - 378/434
b = 56/434
b = 4/31

The equation of the line is y = (63/62)x + 4/31.

4. For the point (9, 1):
Since only one point is given, we cannot determine the slope. Without the slope, we cannot find the equation of the line.