The equation of line passing through (0, 6) and (6, 0) is y = -x + 6
<u><em>Solution:</em></u>
Given that graph of a line passes through the points (0, 6) and (6, 0)
<em><u>The equation of line containing two points is given as:</u></em>
----- eqn 1
Where "m" is the slope of line
Here given two points are (0, 6) and (6, 0)
![(x_1 , y_1) = (0, 6)\\\\(x_2, y_2) = (6, 0)](https://tex.z-dn.net/?f=%28x_1%20%2C%20y_1%29%20%3D%20%280%2C%206%29%5C%5C%5C%5C%28x_2%2C%20y_2%29%20%3D%20%286%2C%200%29)
Let us first find the slope of line
![m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7By_%7B2%7D-y_%7B1%7D%7D%7Bx_%7B2%7D-x_%7B1%7D%7D)
Substituting the values we get,
![m=\frac{0-6}{6-0}=\frac{-6}{6}=-1](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B0-6%7D%7B6-0%7D%3D%5Cfrac%7B-6%7D%7B6%7D%3D-1)
Thus slope of line "m" = -1
Substituting in eqn 1
![y - 6 = -1(x - 0)\\\\y - 6 = -x + 0\\\\y - 6 = -x\\\\y = -x + 6](https://tex.z-dn.net/?f=y%20-%206%20%3D%20-1%28x%20-%200%29%5C%5C%5C%5Cy%20-%206%20%3D%20-x%20%2B%200%5C%5C%5C%5Cy%20-%206%20%3D%20-x%5C%5C%5C%5Cy%20%3D%20-x%20%2B%206)
In standard form we get,
y = -x + 6
x + y = 6
Thus equation of line is found
16)
The formula for finding the volume of a rectangular prism is v=l×w×h
l=length
w=width
h=height
So plug in the numbers and solve normally.
V = 3 × 2 1/2 × 5 1/2
V = 3 × 13 3/4
V = 41 1/4
17)
The formula for finding the volume of a triangular prism is V=1/2(l×w×h)
Plug in the numbers and solve normally.
V = 1/2(4 × 9 1/2 × 8 3/4)
V = 1/2 (4 × 83 1/8)
V = 1/2 (332 1/2)
V = 166 1/4
The predicted time remaining has decreased by 30 years, so the second one would be the answer
I believe that the correct answer to this is 2,905.81
120 different ways hope this helped