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.)

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Step 1: Understand the problem. The given equation is y = 5, which is a horizontal line because the value of y is constant regardless of the value of x. This means that for any x-value, y will always equal 5.

Step 2: Identify the x-values to use for graphing. The problem specifies that x = -3, -2, -1, 0, 1, 2, and 3. These are the x-coordinates for the points we will plot.

Step 3: Calculate the corresponding y-values for each x-value. Since y = 5 for all x-values, the y-coordinate for each point will be 5. This gives the points (-3, 5), (-2, 5), (-1, 5), (0, 5), (1, 5), (2, 5), and (3, 5).

Step 4: Plot the points on a coordinate plane. Place each point on the graph using the x and y coordinates calculated in the previous step. For example, plot (-3, 5), then (-2, 5), and so on.

Step 5: Draw the graph. Connect the points with a straight horizontal line, as the equation y = 5 represents a horizontal line where y is always 5, regardless of x.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

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

Graphing Linear Equations

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

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.

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