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.

Verified step by step guidance

1. Step 1: Start by translating the English sentence into a mathematical equation. The sentence states that the y-value is the difference between four and twice the x-value. This can be written as: $y\; =\; 4\; -\; 2x$.
2. Step 2: Identify the two variables in the equation. Here, $x$ is the independent variable, and $y$ is the dependent variable.
3. Step 3: To graph the equation, create a table of values. Choose a few values for $x$ (e.g., -2, -1, 0, 1, 2) and calculate the corresponding $y$ values using the equation $y\; =\; 4\; -\; 2x$.
4. Step 4: Plot the points from the table of values on a coordinate plane. For example, if $x\; =\; 0$, then $y\; =\; 4$, so one point is (0, 4). Repeat this for all chosen $x$ values.
5. Step 5: Draw a straight line through the plotted points, as the equation $y\; =\; 4\; -\; 2x$ represents a linear relationship. Label the graph appropriately with axes and scales.

Key Concepts

Linear Equations

Linear equations are mathematical statements that express a relationship between two variables, typically in the form y = mx + b, where m is the slope and b is the y-intercept. In this context, the equation represents a straight line on a graph, which can be derived from the given English sentence.

Graphing Equations

Graphing equations involves plotting points on a coordinate plane to visually represent the relationship between the variables. For linear equations, this results in a straight line, which can be created by identifying key points, such as the y-intercept and additional points derived from the equation.

Translating English Sentences to Equations

Translating English sentences into mathematical equations requires understanding the relationships described in the sentence. In this case, phrases like 'the difference between' and 'twice the x-value' indicate how to structure the equation, leading to a mathematical representation of the verbal statement.