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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 because a rectangular coordinate system can indeed provide a geometric representation of an equation with two variables.

Step by step solution

01

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.
02

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.
03

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.

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Most popular questions from this chapter

If you are given a function's graph, how do you determine if the function is even, odd, or neither?

Graph both equations in the same rectangular coordinate system and find all points of intersection. Then show that these ordered pairs satisfy the equations. $$\begin{aligned}x^{2}+y^{2} &=16 \\\x-y &=4\end{aligned}$$

Given an equation in \(x\) and \(y,\) how do you determine if its graph is symmetric with respect to the \(x\) -axis?

Use a graphing utility to graph each function. Use \(a[-5,5,1]\) by [-5,5,1] viewing rectangle. Then find the intervals on which the function is increasing, decreasing, or constant. $$f(x)=x^{3}-6 x^{2}+9 x+1$$

Find and simplify the difference quotient $$\frac{f(x+h)-f(x)}{h}, h \neq 0$$for the given function. $$f(x)=7$$
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