What is the slope of the line that passes through the points (-9, 8) and (−21,10)

-1/6

Step-by-step explanation:

(10 - 8)/(-21 + 9)= 12/-12= -1

y - 8 = -1(x + 9)

y - 8 = -x - 9

y = -x - 1

slope = -1/6

Step-by-step explanation:

To find the slope:

1) find the change in the y values and the change in the x values.

change in y = 8 - 10 = -2

change in x = -9 + 21 = 12

2) divide the change in y and the change in x

slope = -2/12 = -1/6

3. parallelogram

step-by-step explanation:

we turn each of our sides into direction vectors

ab=b-a=(3 - 7, 1 - 0) = (-4, 1)

bc=c-b=(1,6)

cd=d-c=(4,-1)

da=a-d=(-1,-6)

we see how the opposite sides have negated direction vectors; this is characteristic of a parallelogram.   we have congruent sides ab=cd and bc=da with unequal lengths because 1^2+6^2 is different from (-4)^2+1^2.   so it's not a square or a rhombus.  

we check the dot product of direction vectors of adjacent sides.   we have

ab dot bc = -4(1) + 1(6) = 2

that's not zero so the sides are not perpendicular.   we've ruled out rectangle.

the direction vectors indicate two pairs of congruent parallel sides, so we choose parallelogram over trapezoid.

29.5977692753

step-by-step explanation: