In Exercises 47–50, write each English sentence as an equation in two variables. Then graph the equation. y = 5 (Let x = -3, - 2, - 1, 0, 1, 2, and 3.)

Verified step by step guidance

1. Identify the given equation: \( y = 5 \).
2. Recognize that this is a horizontal line where \( y \) is always 5, regardless of the value of \( x \).
3. List the given values for \( x \): -3, -2, -1, 0, 1, 2, and 3.
4. For each value of \( x \), the corresponding \( y \) value is 5, resulting in the points: (-3, 5), (-2, 5), (-1, 5), (0, 5), (1, 5), (2, 5), and (3, 5).
5. Plot these points on a coordinate plane and draw a horizontal line through them to graph the equation.

Key Concepts

Linear Equations

A linear equation in two variables is an equation that can be expressed in the form y = mx + b, where m represents the slope and b represents the y-intercept. This type of equation describes a straight line when graphed on a coordinate plane. Understanding linear equations is essential for translating English sentences into mathematical expressions.

Graphing Techniques

Graphing techniques involve plotting points on a coordinate plane to visually represent equations. For linear equations, you can find points by substituting values for x and calculating the corresponding y values. This process helps in understanding the relationship between the variables and the overall behavior of the equation.

Substitution Method

The substitution method is a technique used to evaluate equations by replacing variables with specific values. In this context, substituting values for x allows you to find the corresponding y values for the equation y = 5. This method is crucial for generating points that can be plotted to graph the equation accurately.