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.)

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 the structure of linear equations is essential for translating English sentences into mathematical expressions.

Graphing a linear equation involves plotting points on a coordinate plane that satisfy the equation. For the equation y = 5, the value of y is constant regardless of x, resulting in a horizontal line at y = 5. Knowing how to plot points and draw lines based on the equation is crucial for visualizing the relationship between the variables.

Substituting values into an equation means replacing the variable with specific numbers to find corresponding outputs. In this case, substituting x values of -3, -2, -1, 0, 1, 2, and 3 into the equation y = 5 will yield the same output for y, demonstrating the concept of a function where y remains constant. This process is fundamental for generating points to graph the equation.