Problem 47 - Precalculus Essentials

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

Answer

The English sentence 'The \(y\) -value is four more than twice the \(x\) -value' translates to the mathematical equation \(y = 2x + 4\). The graph of this equation is a straight line inclined upwards, crossing the \(y\)-axis at \(y = 4\).

Step 1: Formulate the equation

The English sentence provided can be translated into an equation as follows: 'The \(y\) -value is four more than twice the \(x\) -value'. In mathematical terms, this sentence translates to \(y = 2x + 4\). Here, \(y\) represents the \(y\) -value, \(x\) represents the \(x\)-value, 2 is the multiplier (as it's twice the \(x\)-value), and 4 is the value that \(y\) is more than \(2x\).

Step 2: Graph the equation

In this step, the equation \(y = 2x + 4\) needs to be graphed. You start by creating a set of \(x\), \(y\) pairs that satisfy the equation. For example, when \(x = 0\), \(y = 4\), when \(x = 1\), \(y = 6\), and so forth. By plotting these points and drawing a straight line through them, the graph of the equation is created.