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Chapter 1: Problem 48

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.

Short Answer

Expert verified
The English sentence translates to the equation \(y = 4 - 2x\). When graphed, this line will cross the y-axis at \(4\) and slope downwards with a step size of \(2\).

Step by step solution

01

Translate English Sentence into an Algebraic Equation

From the sentence 'The y-value is the difference between four and twice the x-value', the difference between four and twice the x-value translates into an equation as \(y = 4 - 2x\)
02

Identify the Slope and y-intercept

In the equation \(y = 4 - 2x\), the y-intercept is the constant term, which is \(4\). The slope is the coefficient of \(x\), which is \(-2\).
03

Graph the Equation

Start by marking the y-intercept (\(4\)) on the y-axis. Since the slope is \(-2\), for every step to the right along the x-axis, go two steps down. Connect these points to form the line.

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Most popular questions from this chapter

Use the graph of \(y-|4-x|\) to solve each inequality. \(|4-x| \geq 5\)

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Use the strategy for solving word problems, modeling the verbal conditions of the problem with a linear inequality. A local bank charges \(\$ 8\) per month plus 5 e per check. The credit union charges \(\$ 2\) per month plus 8 d per check. How many checks should be written each month to make the credit union a better deal?

Determine whether statement makes sense or does not make sense, and explain your reasoning. I'll win the contest if I can complete the crossword puzzle in 20 minutes plus or minus 5 minutes, so my winning time, \(x\) is modeled by \(|x-20| \leq 5\).

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