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Chapter 1: Problem 67

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.

Short Answer

Expert verified
The statement makes sense as the rectangular coordinate system can indeed provide a geometric representation of an equation in two variables.

Step by step solution

01

Understanding Rectangular Coordinate System

Rectangular coordinate system, also known as the Cartesian coordinate system helps represent equations of two variables in a pictorial or geometrical manner. It consists of two perpendicular lines, namely x-axis and y-axis, which intersect at a point called the origin.
02

Visualization of Equations in the Coordinate System

An equation with two variables is generally represented as y = f(x) where x and y are variables. In a rectangular coordinate system, this equation can be represented as a curve where each (x, y) pair satisfying the equation is a point on the curve.
03

Evaluate the Given Statement

The given statement says - 'The rectangular coordinate system provides a geometric picture of what an equation in two variables looks like.' Based on our understanding of how a rectangular coordinate system works, we can say that this statement makes sense. Equations in two variables (like a linear equation, parabola, circle etc.) can indeed be visualized as a geometric picture or curve in the rectangular coordinate system. Each point on the curve corresponds to a solution of the equation.

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