Jeff wanted to see how many smaller boxes will fit into the larger box. Each small box has a side length of 1.5 inches. The larg
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The given plane has normal vector
Scaling <em>n</em> by a real number <em>t</em> gives a set of vectors that span an entire line through the origin. Translating this line by adding the vector <2, 1, 1> makes it so that this line passes through the point (2, 1, 1). So this line has equation
This line passes through (2, 1, 1) when <em>t</em> = 0, and the line intersects with the plane when
which corresponds the point (3, -1, 1) (simply plug <em>t</em> = 1 into the coordinates of ).
So the distance between the plane and the point is the distance between the points (2, 1, 1) and (3, -1, 1):
Hello!
Find the coordinate where x = -1:
At x = -1, y = 1, so the coordinate is (-1, 1).
Find the coordinate where x = 2:
At x = 2, y = -2, so the coordinate is (2, -2).
Find the rate of change between the points using the slope formula:
Plug in the coordinates above:
Simplify:
Thus, the rate of change between the points is -1.