Ch. 1 - Equations and Inequalities

Blitzer8th EditionCollege AlgebraISBN: 9780136970514Not the one you use?Change textbook

Blitzer 8th Edition

Ch. 1 - Equations and Inequalities

Problem 47a

Chapter 2, Problem 47a

Write each English sentence as an equation in two variables. Then graph the equation. The y-value is four more than twice the x-value.

Verified step by step guidance

Step 1: Start by translating the English sentence into a mathematical equation. The sentence states that 'The y-value is four more than twice the x-value.' This can be written as:

y = 2x + 4

Step 2: Identify the two variables in the equation. Here,

x

is the independent variable (input), and

y

is the dependent variable (output).

Step 3: To graph the equation, create a table of values. Choose a few values for

x

(e.g., -2, -1, 0, 1, 2) and calculate the corresponding

y

values using the equation

y = 2x + 4

Step 4: Plot the points from the table of values on a coordinate plane. For example, if

x = 0

, then

y = 4

, so plot the point (0, 4). Repeat this for all chosen

x

values.

Step 5: Draw a straight line through the plotted points, as the equation

y = 2x + 4

represents a linear relationship. Label the graph with the equation for clarity.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Linear Equations

Linear equations are mathematical statements that express a relationship between two variables, typically in the form y = mx + b, where m is the slope and b is the y-intercept. Understanding linear equations is essential for translating verbal statements into mathematical form, as they represent straight lines when graphed.

Translating English Sentences to Equations

Translating English sentences into equations involves identifying the mathematical relationships described in the text. This requires recognizing keywords and phrases that indicate operations, such as 'more than' or 'twice,' and converting them into algebraic expressions that accurately represent the relationships between the variables.

Graphing Linear Equations

Graphing linear equations involves plotting points on a coordinate plane that satisfy the equation. By determining key values, such as the slope and y-intercept, one can draw a straight line that represents all solutions to the equation. This visual representation helps in understanding the relationship between the variables and analyzing their behavior.

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Related Practice

Textbook Question

In Exercises 45–47, solve each formula for the specified variable. T = (A-P)/Pr for P

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Textbook Question

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. (x - 2)/2x + 1 = (x + 1)/x

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Textbook Question

Solve each equation in Exercises 41–60 by making an appropriate substitution. x^(-2) - x^(-1) - 6 = 0

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Textbook Question

Write each English sentence as an equation in two variables. Then graph the equation. The y-value is the difference between four and twice the x-value.

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Textbook Question

In Exercises 35–54, solve each formula for the specified variable. Do you recognize the formula? If so, what does it describe? S = P + Prt for r

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Textbook Question

Perform the indicated operations and write the result in standard form. $$\sqrt{-8}$ $\left$( $\sqrt{-3}$ - $\sqrt{-5}$ $\right$)$

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