Problem 47 - Algebra and Trigonometry

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 translated equation is \(y = 2x + 4\). The graph of the equation is a straight line passing through the points (-1, 2), (0, 4) and (1, 6).

Step 1: Translate the sentence into an equation

The sentence can be interpreted as: \(y\) equals twice \(x\), plus 4. This can be written as: \(y = 2x + 4\)

Step 2: Make a table of values

To draw a graph we need a set of points \((x, y)\) that satisfies the equation \(y = 2x + 4\). Usually, choosing a few values for \(x\) and then calculating the corresponding \(y\) values is an efficient way to find these points. For example, choose \(x = -1, 0, 1\). For \(x = -1\), \(y = 2*-1 + 4 = 2\). For \(x = 0\), \(y = 2*0 + 4 = 4\). For \(x = 1\), \(y = 2*1 + 4 = 6\). So, the points are: (-1, 2), (0, 4) and (1, 6).

Step 3: Draw the graph

Plot the points (-1, 2), (0, 4) and (1, 6) on a coordinate plane. Draw a line through the points extending beyond them in both directions. This represents all the solutions of the equation.