As a math teacher, allow me to address the statement in question.
The statement that "an equation allows you to find the x- and y-coordinates of any point on the xy-plane" suggests that given an equation with x and y as variables, we can determine pairs of x and y that satisfy the equation. By doing so, those pairs can be represented as points on the xy-plane, also called the Cartesian plane.
Let's consider a simple example with a linear equation:
y = 2x + 3
This equation expresses a relationship between x and y. For any value of x that you choose, you can find a corresponding value of y using this equation. By plotting all such pairs (x, y) that satisfy the equation, we create a graph on the xy-plane which—in the case of this example—would be a straight line.
If we take a more complex example, such as a quadratic equation like:
y = x^2 - 4x + 4
This equation also defines a set of points (x, y) that can be plotted on the xy-plane, and in this case, the result would be a parabola.
In both of these examples, and indeed for any equation involving x and y, we see that they define a set of points on the xy-plane. So for each x-value, there's a corresponding y-value that satisfies the equation, and these pairs can be graphed as points on the plane. Therefore, we can confirm that the statement is indeed true.
Each graph is a visual representation of all the (x, y) pairs that fulfill the given equation. The shape of the graph depends on the type of equation: Linear equations result in lines, quadratic equations result in parabolas, and so on for other types of functions.
So, the correct answer to the question is:
A. True
The equation defines a relationship between x and y, and this relationship can be represented visually by plotting the pairs of values on the xy-plane, resulting in a graph that shows all the combinations of x and y that make the equation true.
