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Chapter 1: Problem 64

Explain how to graph an equation in the rectangular coordinate system.

Short Answer

Expert verified
To graph an equation in a rectangular coordinate system, understand the equation, prepare a table of values, plot the points, draw the resulting curve, and validate the graph.

Step by step solution

01

Understand the Equation

An equation gives a relationship between variables, often x and y in a two-dimensional coordinate system. A common form of such equations is \(y = f(x)\), where y changes in response to changes in the x-variable following the rule defined by function \(f\).
02

Prepare a Table of Values

Choose several values for \(x\) and find the corresponding \(y\)-values using the equation. Prepare a table with columns for \(x\) and \(y\), and write down each pair of corresponding values.
03

Plot Points onto the Coordinate System

On the rectangular coordinate system, plot the (\(x,y\)) pairs identified in step 2. The x-coordinate corresponds to the horizontal position, with positive values to the right and negative values to the left of the origin. The y-coordinate corresponds to the vertical position, with positive values above and negative values below the origin.
04

Draw the Curve

Once a sufficient number of points are plotted, they can be used to draw a line or curve. The exact number of points needed often depends on the complexity of the function. In most cases, the curve will be a straight line for a linear equation and a parabola for a quadratic equation.
05

Check the Graph

Finally, validate the plot by picking a point not used in step 2, substitute the \(x\)-coordinate into the function to get a \(y\)-value, and check that the (\(x,y\)) pair lies on the graph.

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Most popular questions from this chapter

Solve for \(t: s=-16 t^{2}+v_{0} t\)

One of the best ways to learn how to solve a word problem in algebra is to design word problems of your own. Creating a word problem makes you very aware of precisely how much information is needed to solve the problem. You must also focus on the best way to present information to a reader and on how much information to give. As you write your problem, you gain skills that will help you solve problems created by others. The group should design five different word problems that can be solved using linear equations. All of the problems should be on different topics. For example, the group should not have more than one problem on simple interest. The group should turn in both the problems and their algebraic solutions.

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When the sum of 1 and twice a negative number is subtracted from twice the square of the number, 0 results. Find the number.

Solve each formula for the specified variable. Do you recognize the formula? If so, what does it describe? $$s=P+P r t \text { for } r$$
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