Ch. 1 - Equations and Inequalities

Blitzer8th EditionCollege AlgebraISBN: 9780136970514Non è quello che usi tu?Cambia libro di testo

Blitzer 8th Edition

Ch. 1 - Equations and Inequalities

Problema 51a

Capitolo 2, Problema 51a

Write each English sentence as an equation in two variables. Then graph the equation. y = 5 (Let x = -3, - 2, - 1, 0, 1, 2, and 3.)

Guida verificata passo dopo passo

Step 1: Understand the problem. The given equation is y = 5, which is a horizontal line because the value of y is constant regardless of the value of x. This means that for any x-value, y will always equal 5.

Step 2: Identify the x-values to use for graphing. The problem specifies that x = -3, -2, -1, 0, 1, 2, and 3. These are the x-coordinates for the points we will plot.

Step 3: Calculate the corresponding y-values for each x-value. Since y = 5 for all x-values, the y-coordinate for each point will be 5. This gives the points (-3, 5), (-2, 5), (-1, 5), (0, 5), (1, 5), (2, 5), and (3, 5).

Step 4: Plot the points on a coordinate plane. Place each point on the graph using the x and y coordinates calculated in the previous step. For example, plot (-3, 5), then (-2, 5), and so on.

Step 5: Draw the graph. Connect the points with a straight horizontal line, as the equation y = 5 represents a horizontal line where y is always 5, regardless of x.

Risposta video verificata per un problema simile:

Questa soluzione video è stata consigliata dai nostri tutor come utile per risolvere questo problema.

Durata del video:

Concetti chiave

Ecco i concetti essenziali che devi comprendere per rispondere correttamente alla domanda.

Linear Equations

A linear equation in two variables is an equation that can be expressed in the form y = mx + b, where m represents the slope and b represents the y-intercept. This type of equation describes a straight line when graphed on a coordinate plane. Understanding the structure of linear equations is essential for translating English sentences into mathematical expressions.

Video consigliato:

06:00

Categorizing Linear Equations

Graphing Linear Equations

Graphing a linear equation involves plotting points on a coordinate plane that satisfy the equation. For the equation y = 5, the value of y is constant regardless of x, resulting in a horizontal line at y = 5. Knowing how to plot points and draw lines based on the equation is crucial for visualizing the relationship between the variables.

Video consigliato:

06:00

Categorizing Linear Equations

Substituting Values

Substituting values into an equation means replacing the variable with specific numbers to find corresponding outputs. In this case, substituting x values of -3, -2, -1, 0, 1, 2, and 3 into the equation y = 5 will yield the same output for y, demonstrating the concept of a function where y remains constant. This process is fundamental for generating points to graph the equation.

Video consigliato:

5:48

Solving Systems of Equations - Substitution

Pratica correlata

Domanda del libro di testo

Solve each equation in Exercises 41–60 by making an appropriate substitution. $x^{\frac{2}{5}} + x^{\frac{1}{5}} - 6 = 0$

593

views

Domanda del libro di testo

In Exercises 37–52, perform the indicated operations and write the result in standard form. (3√-5)(- 4√-12)

174

views

Domanda del libro di testo

Solve each equation in Exercises 47–64 by completing the square. $x^{2} - 6 x - 11 = 0$

965

views

Domanda del libro di testo

In Exercises 35–54, solve each formula for the specified variable. Do you recognize the formula? If so, what does it describe? A = 2lw + 2lh + 2wh for h

665

views

Domanda del libro di testo

In Exercises 51–58, solve each compound inequality. 6 < x + 3 < 8

1161

views

Domanda del libro di testo

Exercises 41–60 contain rational equations with variables in denominators. For each equation, a. write the value or values of the variable that make a denominator zero. These are the restrictions on the variable. b. Keeping the restrictions in mind, solve the equation. 2/(x - 2) = x/(x - 2) - 2

841

views