4.Determine which point does not lie on the graph of the line y=x-3

a. (-10, 13)
b. (-10-13)
c. (-8, -11)
A?

8. What is the best model for a tabletop?
a. plane
b. line
c. point
d. none of these
A?

40. If 2 points lie in a plane, the line containing them ______
a. intersects the plane once
b. lies in the same plane
c. is skew
d. does not intersect the plane
A?

41. A plane and a point not on the plane are _____ coplanar.
a. always
b. sometimes
c. never
d. not enough information to tell
C?

Thanks

4. To determine which point does not lie on the graph of the line y = x - 3, you need to substitute the coordinates of each point into the equation and check if it satisfies the equation.

Let's start with option a. (-10, 13):
Substituting the coordinates into the equation, we get:
13 = -10 - 3
13 = -13
This equation is not true, so (-10, 13) does not lie on the graph of the line.

Now let's check option b. (-10, -13):
Substituting the coordinates into the equation, we get:
-13 = -10 - 3
-13 = -13
This equation is true, so (-10, -13) lies on the graph of the line.

Finally, let's check option c. (-8, -11):
Substituting the coordinates into the equation, we get:
-11 = -8 - 3
-11 = -11
This equation is true, so (-8, -11) lies on the graph of the line.

Therefore, the point that does not lie on the graph of the line y = x - 3 is option A, (-10, 13).

8. To determine the best model for a tabletop, we need to consider the properties of a tabletop. A tabletop is a two-dimensional object that is flat and has width and length.
Among the given options: (a) plane, (b) line, (c) point, and (d) none of these, the best model for a tabletop would be the option (a) plane. A plane is a flat, two-dimensional surface that extends infinitely in all directions. This accurately represents the properties of a tabletop.

40. If two points lie in a plane, the line containing them lies in the same plane. Therefore, the correct answer is (b) lies in the same plane.

41. A plane and a point not on the plane are never coplanar. Coplanar refers to objects that lie in the same plane. Since a point not on the plane does not lie within the same two-dimensional surface, it cannot be coplanar with the plane. Therefore, the correct answer is (c) never.