Using the general format of a line, y = mx + c,
Where m = slope of the line, c = vertical intercept.
y = -3x -3, comparing to y = mx + c
Slope, m = -3, vertical intercept, c = -3.
For a negative slope, the line would be falling downwards from the left hand side of graph sheet to right hand side.
Slope = -3,
Vertical or y intercept is the point it cuts across the y axis, at this point, x = 0
y intercept = (0, -3)
x intercept, at this point, the value of y is zero.
y = -3x - 3
0 = -3x - 3
0 + 3x = -3
3x = -3
x = -3/3
x = -1.
x intercept = (-1, 0)
So we would plot the points (0, -3) and (-1, 0)
See attached picture for sketch of the line y = -3x - 3.
She curled an 8 inch by 10 inch rectangular piece of paper to form an open cylinder. A height of that cylinder is h = 10 in. Then 8 inches will represent the circumference of the base of the cylinder ( or the circumference of the circle, which represents the base ). Therefore: C = 2 r π, or: 8 = 2 r π. Now we can also calculate the radius of the base:
r = 8 : 2 π = 8 : 2 * 3.14 = 8 : 6.28 ≈ 1.27 in.
Answer: 8 inches will be the circumference of the base of the cylinder.
is the disk of radius 1 parallel to the
-plane and lying in the plane
. Parameterize this surface by

with
and
. Take the normal vector to
to be

(the orientation doesn't matter because this is a scalar surface integral)
Then

