Problem 67 - College Algebra

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

Answer

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

Step 1: 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.

Step 2: 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.

Step 3: 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.