Final answer:
The set of points satisfying an equation is known as the solution set, with examples including points on a line for linear equations and points on a parabola for quadratic equations. These points are defined using coordinate systems.
Step-by-step explanation:
The set of points whose coordinates satisfy an equation is called the solution set of the equation. For example, the graph of a linear equation of the form y = a + bx is a straight line, and the solution set in this case is the set of all points (x, y) that lie on that line. Another example relevant to quadratic equations is that the solution set consists of all the points that coincide with the parabola described by the quadratic function.
In the context of plotting data and finding lines of best fit, the sample means of the x values and the y values are x and y, respectively. The best-fit line will always pass through the point (x, y), providing a point that is part of the line's solution set. Systems of coordinates, such as latitude and longitude or Cartesian coordinates (x, y, z), are used to define the position of points and effectively describe their location within the solution set.