Problem 48
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.
Step-by-Step Solution
Verified Answer
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 \(2\).
1Step 1: 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 \(y = 4 - 2x\)
2Step 2: 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 \(-2\).
3Step 3: 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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