Problem 47
Question
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.
Step-by-Step Solution
Verified Answer
The English sentence can be translated into the equation \(y = 2x + 4\). When this equation is graphed, it is a straight line that passes through the points (-2, 0), (0, 4), and (2, 8).
1Step 1: Translate the English sentence into an equation
The sentence ‘The y-value is four more than twice the x-value’ can be written as the equation \(y = 2x + 4\).
2Step 2: Get the values to plot the graph
To draw the graph of this equation, it's necessary to get some values of x and calculate the corresponding y. Let's choose a few arbitrary x-values, for example, -2, 0, and 2, and then calculate the corresponding y-values using the given equation \(y = 2x + 4\).
3Step 3: Plot the graph
The values obtained should be plotted on a graph. The x-values are represented on the horizontal axis and the y-values on the vertical axis. So, points (-2, 0), (0, 4), and (2, 8) should be plotted and connected with a straight line to complete the graph.
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