Problem 67
Question
Determine whether each statement makes sense or does not make sense, and explain your reasoning. The rectangular coordinate system provides a geometric picture of what an equation in two variables looks like.
Step-by-Step Solution
Verified Answer
The statement makes sense because a rectangular coordinate system can indeed provide a geometric representation of an equation with two variables.
1Step 1: Understanding the Rectangular Coordinate System and Equations in Two Variables
A rectangular coordinate system is a two-dimensional plane-based system where each point on this plane is associated with a unique pair of values (x, y). An equation with two variables, say, y = x + 3 or y = 2x^2, is a rule that vertically relates each x-value to exactly one y-value.
2Step 2: Visualizing Equations in the Rectangular Coordinate System
An equation in two variables can be graphed on a rectangular coordinate system. For example, the equation y = x + 3 will appear as a straight line on the graph, where each point on this line indicates that the x and y coordinates at that point satisfy the equation y = x + 3.
3Step 3: Reasoning the Statement
Since we can visually depict the relation between x and y values of an equation through a graph on the rectangular coordinate system, the statement does make sense.
Other exercises in this chapter
Problem 67
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