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2 for linear (powers of 1), 3 for quadratic (powers of 2), etc

Q: How many point will determine the line?

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A point lies on a line if the coordinates of the point satisfy the equation of the line.

Yes its on the line.

A single point cannot determine the slope of a straight line. It can, therefore, have any slope at all.

Yes since 3 non-collinear points determine a plane. Of course one can take any two of the three points and draw a line between them. There are an infinite number of planes going through this line. Now pick on more point, not on the line, and those three points uniquely determine a plane.

Two distinct (different) points are needed to determine a line.

Related questions

A point lies on a line if the coordinates of the point satisfy the equation of the line.

You need two points to determine a line. A single point can have an infinite number of lines passing through it.

Substitute the coordinates of the point into the equation of the line. If the equation is still valid then the point is on the line; if not then it is not.

Two points determine a line. Also there is one and only line perpendicular to given line through a given point on the line,. and There is one and only line parallel to given line through a given point not on the line.

Yes its on the line.

A single point cannot determine the slope of a straight line. It can, therefore, have any slope at all.

Yes since 3 non-collinear points determine a plane. Of course one can take any two of the three points and draw a line between them. There are an infinite number of planes going through this line. Now pick on more point, not on the line, and those three points uniquely determine a plane.

Two distinct (different) points are needed to determine a line.

Substitute the x coordinate into the equation for x and calculate y. If the formla gives the same y value as the coordinates, the point is on the line. If it is diffent, it is not on the line.

Two

Any three points will determine a plane, provided they are not collinear. If you pick any two points, you can draw a line to connect them. An infinite number of planes can be drawn that include the line. But if you pick a third point that does not lie on the line. There will be exactly one plane that will contain the line and that point you added last. Only oneplane can contain the line, which was determined by the first two points, and the last point.

In order to draw a straight line, two unique ordered pairs are needed. This is because two unique points determine a line and an ordered pair represents a point.